A stochastic numerical analysis of a multirotor was performed considering the rotational speed fluctuation to investigate the acoustic characteristics. To validate the analysis, the noise was measured in an anechoic chamber at different azimuth angles (from 0° to 45°) and polar angles (from 0° to 67.5°) in revolutions per minute (RPM) assuming a multirotor hovering maneuver. Frequency and amplitude modulation characteristics due to RPM fluctuations were observed despite the considered hovering condition. Moreover, an azimuthal noise directivity pattern in a circular shape was observed, which corresponds to the collapse of the phase effect due to the RPM fluctuation of each rotor. In the existing numerical studies, the RPM fluctuation could not be considered due to the high computational cost. In this study, a random process was applied to reflect the RPM fluctuation effects through a validated multirotor noise assessment framework. To perform the stochastic analysis, ensemble averaging, a concept of random process, was applied to analyze the acoustic effects of the multirotor considering generalized RPM fluctuations. A quantitative analysis was conducted considering the spectrum, azimuthal directivity, polar directivity, and noise signal similarity. The results indicated that the proposed stochastic analysis could effectively predict the multirotor noise by taking into account the RPM fluctuation effect.
References
1.
B.
Aydin
, “Public acceptance of drones: Knowledge, attitudes, and practice
,” Technol. Soc.
59
, 101180
(2019
).2.
J. V.
Foster
, L. J.
Miller
, R. C.
Busan
, S.
Langston
, and D.
Hartman
, “Recent nasa wind tunnel free-flight testing of a multirotor unmanned aircraft system
,” in AIAA Scitech 2020 Forum
(American Institute of Aeronautics and Astronautics, 2020
), p. 1504
.3.
N.
Intaratep
, W. N.
Alexander
, W. J.
Devenport
, S. M.
Grace
, and A.
Dropkin
, “Experimental study of quadcopter acoustics and performance at static thrust conditions
,” in 22nd AIAA/CEAS Aeroacoustics Conference
(American Institute of Aeronautics and Astronautics, 2016
), p. 2873
.4.
F.
Christiansen
, L.
Rojano-Doñate
, P. T.
Madsen
, and L.
Bejder
, “Noise levels of multi-rotor unmanned aerial vehicles with implications for potential underwater impacts on marine mammals
,” Front. Mar. Sci.
3
, 277
(2016
).5.
R.
Islam
, A.
Stimpson
, and M.
Cummings
, Small Uav Noise Analysis
(Humans and Autonomy Laboratory, Duke University
, Durham, NC
, 2017
).6.
J.
Ivošević
, E.
Ganić
, A.
Petošić
, and T.
Radišić
, “Comparative UAV noise-impact assessments through survey and noise measurements
,” Int. J. Environ. Res. Public Health
18
, 6202
(2021
).7.
N.
Kloet
, S.
Watkins
, and R.
Clothier
, “Acoustic signature measurement of small multi-rotor unmanned aircraft systems
,” Int. J. Micro Air Vehicles
9
, 3
–14
(2017
).8.
S.
Watkins
, J.
Burry
, A.
Mohamed
, M.
Marino
, S.
Prudden
, A.
Fisher
, N.
Kloet
, T.
Jakobi
, and R.
Clothier
, “Ten questions concerning the use of drones in urban environments
,” Build. Environ.
167
, 106458
(2020
).9.
G.
Leventhall
, “Low frequency noise. what we know, what we do not know, and what we would like to know
,” J. Low Frequency Noise, Vib. Active Control
28
, 79
–104
(2009
).10.
I.
Circular
, 328, Unmanned Aircraft Systems (UAS)
[International Civil Aviation Organization (ICAO)
, Montreal, Canada
, 2011
].11.
D.
Miljković
, “Methods for attenuation of unmanned aerial vehicle noise
,” in 41st International Convention on Information and Communication Technology, Electronics and Microelectronics (MIPRO)
(IEEE
, 2018
), pp. 0914
–0919
.12.
S. A.
Rizzi
, Urban Air Mobility Noise: Current Practice, Gaps, and Recommendations
(National Aeronautics and Space Administration
, Langley Research Center
, 2020
).13.
A. W.
Christian
and R.
Cabell
, “Initial investigation into the psychoacoustic properties of small unmanned aerial system noise
,” in 23rd AIAA/CEAS Aeroacoustics Conference
(American Institute of Aeronautics and Astronautics, 2017
), p. 4051
.14.
D. Y.
Gwak
, D.
Han
, and S.
Lee
, “Sound quality factors influencing annoyance from hovering UAV
,” J. Sound Vib.
489
, 115651
(2020
).15.
A. J.
Torija
and C.
Clark
, “A psychoacoustic approach to building knowledge about human response to noise of unmanned aerial vehicles
,” Int. J. Environ. Res. Public Health
18
, 682
(2021
).16.
B.
Schäffer
, R.
Pieren
, K.
Heutschi
, J. M.
Wunderli
, and S.
Becker
, “Drone noise emission characteristics and noise effects on humans-a systematic review
,” Int. J. Environ. Res. Public Health
18
, 5940
(2021
).17.
R.
McKay
and M. J.
Kingan
, “Multirotor unmanned aerial system propeller noise caused by unsteady blade motion
,” in 25th AIAA/CEAS Aeroacoustics Conference
(American Institute of Aeronautics and Astronautics, 2019
), p. 2499
.18.
D.
Han
, D. Y.
Gwak
, and S.
Lee
, “Noise prediction of multi-rotor UAV by RPM fluctuation correction method
,” J. Mech. Sci. Technol.
34
, 1429
–1443
(2020
).19.
D.
Kim
, J.
Ko
, V.
Saravanan
, and S.
Lee
, “Stochastic analysis of a single-rotor to quantify the effect of RPS variation on noise of hovering multirotors
,” Appl. Acoust.
182
, 108224
(2021
).20.
J.
Ko
, J.
Kim
, and S.
Lee
, “Computational study of wake interaction and aeroacoustic characteristics in multirotor configurations
,” in INTER-NOISE and NOISE-CON Congress and Conference Proceedings
(Institute of Noise Control Engineering
, 2019
), Vol. 259
, pp. 5145
–5156
.21.
H.
Lee
and D.
Lee
, “Rotor interactional effects on aerodynamic and noise characteristics of a small multirotor unmanned aerial vehicle
,” Phys. Fluids
32
, 047107
(2020
).22.
G.
Barakos
, R.
Steijl
, K.
Badcock
, and A.
Brocklehurst
, “Development of CFD capability for full helicopter engineering analysis
,” in 31st European Rotorcraft Forum
(The Council of European Aerospace Societies
, Florence, Italy
, 2005
), p. 91
.23.
R.
Steijl
, G.
Barakos
, and K.
Badcock
, “A framework for CFD analysis of helicopter rotors in hover and forward flight
,” Int. J. Numer. Methods Fluids
51
, 819
–847
(2006
).24.
J.
Ko
and S.
Lee
, “Numerical investigation of inter-rotor spacing effects on wake dynamics of coaxial rotors
,” J. Aircraft
58
, 363
–373
(2021
).25.
P.
Ventura Diaz
and S.
Yoon
, “High-fidelity computational aerodynamics of multi-rotor unmanned aerial vehicles
,” in AIAA Aerospace Sciences Meeting
(American Institute of Aeronautics and Astronautics, 2018
), p. 1266
.26.
T.
Dbouk
and D.
Drikakis
, “Quadcopter drones swarm aeroacoustics
,” Phys. Fluids
33
, 057112
(2021
).27.
W.
Johnson
, C.
Silva
, and E.
Solis
, “Concept vehicles for VTOL air taxi operations
,” in American Helicopter Society (AHS) Specialists Conference on Aeromechanics Design for Transformative Vertical Flight (2018
).28.
Z.
Jia
and S.
Lee
, “Acoustic analysis of a quadrotor evtol design via high-fidelity simulations
,” in 25th AIAA/CEAS Aeroacoustics Conference
(American Institute of Aeronautics and Astronautics, 2019
), p. 2631
.29.
P.
Ventura Diaz
and S.
Yoon
, “Computational study of NASA'S quadrotor urban air taxi concept
,” in AIAA SciTech 2020 Forum
(American Institute of Aeronautics and Astronautics, 2020
), p. 0302
.30.
J.
Ko
, J.
Jeong
, H.
Cho
, and S.
Lee
, “Real-time prediction framework for frequency-modulated multirotor noise
,” (unpublished).31.
D.
Weitsman
, J. H.
Stephenson
, and N. S.
Zawodny
, “Effects of flow recirculation on acoustic and dynamic measurements of rotary-wing systems operating in closed anechoic chambers
,” J. Acoust. Soc. Am.
148
, 1325
–1336
(2020
).32.
N. A.
Pettingill
, N. S.
Zawodny
, C.
Thurman
, and L. V.
Lopes
, “Acoustic and performance characteristics of an ideally twisted rotor in hover
,” in AIAA Scitech 2021 Forum
(American Institute of Aeronautics and Astronautics, 2021
), p. 1928
.33.
N. S.
Zawodny
, D. D.
Boyd
, Jr., and C. L.
Burley
, “Acoustic characterization and prediction of representative, small-scale rotary-wing unmanned aircraft system components
,” in American Helicopter Society (AHS) Annual Forum (2016
).34.
Z.
Zuo
, “Trajectory tracking control design with command-filtered compensation for a quadrotor
,” IET Control Theory Appl.
4
, 2343
–2355
(2010
).35.
B.
Davoudi
and K.
Duraisamy
, “A hybrid blade element momentum model for flight simulation of rotary wing unmanned aerial vehicles
,” in AIAA Aviation 2019 Forum
(American Institute of Aeronautics and Astronautics, 2019
), p. 2823
.36.
D. A.
Peters
and C. J.
He
, “Correlation of measured induced velocities with a finite-state wake model
,” J. Am. Helicopter Soc.
36
, 59
–70
(1991
).37.
T.
Beddoes
, “A wake model for high resolution airloads
,” in International Conference on Rotorcraft Basic Research
(1985
).38.
E.
Greenwood
II, Fundamental Rotorcraft Acoustic Modeling from Experiments (FRAME
) (University of Maryland
, College Park
, 2011
).39.
C.
Porter
, M.
Rennie
, and E.
Jumper
, “Computation of the aero-optical environment of a helicopter using prescribed-wake methods
,” AIAA J.
53
, 532
–541
(2015
).40.
Y.
Murakami
, Y.
Tanabe
, S.
Saito
, and H.
Sugawara
, “A new appreciation of prescribed wake models for cfd analysis in view of aeroacoustic applications
,” in (37th European Rotorcraft Forum, 2011
).41.
A.
Najafi-Yazdi
, G. A.
Brès
, and L.
Mongeau
, “An acoustic analogy formulation for moving sources in uniformly moving media
,” Proc. R. Soc. A
467
, 144
–165
(2011
).42.
D.
Casalino
, “An advanced time approach for acoustic analogy predictions
,” J. Sound Vib.
261
, 583
–612
(2003
).43.
G.
Brès
, K.
Brentner
, G.
Perez
, and H.
Jones
, “Maneuvering rotorcraft noise prediction
,” J. Sound Vib.
275
, 719
–738
(2004
).44.
L. V.
Lopes
, “Compact assumption applied to monopole term of Farassat's formulations
,” J. Aircraft
54
, 1649
–1663
(2017
).45.
M.
Natrella
, NIST/Sematech e-Handbook of Statistical Methods
(NIST/Sematech
, 2010
), Vol. 49
.46.
Z.
Wang
, A. C.
Bovik
, H. R.
Sheikh
, and E. P.
Simoncelli
, “Image quality assessment: From error visibility to structural similarity
,” IEEE Trans. Image Process.
13
, 600
–612
(2004
).47.
R. W.
Deters
, S.
Kleinke
, and M. S.
Selig
, “Static testing of propulsion elements for small multirotor unmanned aerial vehicles
,” in American Helicopter Society (AHS) International Annual Forum and Technology Display
(American Institute of Aeronautics and Astronautics, 2017
), p. 3743
.48.
C.
Russell
, J.
Jung
, G.
Willink
, and B.
Glasner
, “Wind tunnel and hover performance test results for multicopter UAS vehicles
,” in AHS 72nd Annual Forum
(American Institute of Aeronautics and Astronautics, 2016
), pp. 16
–19
.49.
K. A.
Pascioni
, S. A.
Rizzi
, and N.
Schiller
, “Noise reduction potential of phase control for distributed propulsion vehicles
,” in AIAA Scitech 2019 Forum
(American Institute of Aeronautics and Astronautics, 2019
), p. 1069
.50.
J.
Johnston
, R.
Donham
, and W.
Guinn
, “Propeller signatures and their use
,” J. Aircraft
18
, 934
–942
(1981
).51.
B.
Magliozzi
, “Synchrophasing for cabin noise reduction of propeller-driven airplanes
,” in 8th Aeroacoustics Conference
(American Institute of Aeronautics and Astronautics, 1983
), p. 717
.52.
K.
Pascioni
and S. A.
Rizzi
, “Tonal noise prediction of a distributed propulsion unmanned aerial vehicle
,” in 2018 AIAA/CEAS Aeroacoustics Conference
(American Institute of Aeronautics and Astronautics, 2018
), p. 2951
.53.
B.
Smith
, R.
Niemiec
, and F.
Gandhi
, “A comparison of multicopter noise characteristics with increasing number of rotors
,” in 76th Annual Forum of the Vertical Flight Society
, Virtual (2020
).54.
G.
Shujun
, L.
Yang
, S.
Taoyong
, and X.
Xice
, “Noise attenuation of quadrotor using phase synchronization method
,” Aerosp. Sci. Technol.
118
, 107018
(2021
).55.
S.
Guan
, Y.
Lu
, T.
Su
, and X.
Xu
, “Noise attenuation of quadrotor using phase synchronization method
,” Aerosp. Sci. Technol.
118
, 107018
(2021
).56.
A. J.
Landgrebe
, “The wake geometry of a hovering helicopter rotor and its influence on rotor performance
,” J. Am. Helicopter Soc.
17
, 3
–15
(1972
).© 2021 Author(s). Published under an exclusive license by AIP Publishing.
2021
Author(s)
You do not currently have access to this content.