Abstract

Urban aerial mobility (UAM) vehicles with multipropeller configurations have attracted considerable attention in recent years. However, previous investigations have mainly focused on the aerodynamic noise from individual propellers, with limited focus on the fuselage’s sound scattering effects which can alter the far-field noise directivity. In this work, an efficient boundary element solver for sound scattering was developed to fill this gap. The solver employs hierarchical matrices to save computational cost. The benchmark examples showed high accuracy and good scalability. A representative vehicle model was then chosen, and the propeller noise was simulated using rotating sources. Results show that the shielding effect in the fuselage/propeller configuration can produce an apparent noise reduction and redirect sound energy distribution, suggesting the importance of considering the fuselage in low-noise UAM development.

References

1.
Zhou
,
T.
,
Jiang
,
H.
,
Sun
,
Y.
,
Fattah
,
R. J.
,
Zhang
,
X.
,
Huang
,
B.
, and
Cheng
,
L.
,
2019
, “
Acoustic Characteristics of a Quad-Copter Under Realistic Flight Conditions
,”
25th AIAA/CEAS Aeroacoustics Conference
,
Delft, The Netherlands
,
May 20–23
, p.
2587
.
2.
Hu
,
H.
,
Yang
,
Y.
,
Liu
,
Y.
,
Liu
,
X.
, and
Wang
,
Y.
,
2021
, “
Aerodynamic and Aeroacoustic Investigations of Multi-Copter Rotors With Leading Edge Serrations During Forward Flight
,”
Aerosp. Sci. Technol.
,
112
, p.
106669
.
3.
Casalino
,
D.
,
Grande
,
E.
,
Romani
,
G.
,
Ragni
,
D.
, and
Avallone
,
F.
,
2021
, “
Definition of a Benchmark for Low Reynolds Number Propeller Aeroacoustics
,”
Aerosp. Sci. Technol.
,
113
(
3
), p.
106707
.
4.
Eaton
,
J.
, and
Regan
,
B.
,
1996
, “
Application of the Finite Element Method to Acoustic Scattering Problems
,”
AIAA. J.
,
34
(
1
), pp.
29
34
.
5.
Yin
,
J.
,
2019
, “
Investigation of Rotor Noise Shielding Effects by the Helicopter Fuselage in Forward Flight
,”
J. Aircr.
,
56
(
4
), pp.
1677
1688
.
6.
Jiang
,
H.
,
Zhang
,
X.
, and
Huang
,
X.
,
2019
, “
Reduced-Basis Boundary Element Method for Efficient Broadband Acoustic Simulation
,”
J. Sound. Vib.
,
456
(
3
), pp.
374
385
.
7.
Jiang
,
H.
,
Zhou
,
T.
,
Fattah
,
R. J.
,
Zhang
,
X.
, and
Huang
,
X.
,
2019
, “
Multi-rotor noise scattering by a drone fuselage
,”
25th AIAA/CEAS Aeroacoustics Conference
,
Delft, The Netherlands
,
May 20–23
.
8.
Higgins
,
R. J.
,
Barakos
,
G. N.
,
Shahpar
,
S.
, and
Tristanto
,
I.
,
2021
, “
A Computational Fluid Dynamic Acoustic Investigation of a Tiltwing Evtol Concept Aircraft
,”
Aerosp. Sci. Technol.
,
111
(
5
), p.
106571
.
9.
Bian
,
H.
,
Fattah
,
R.
,
Zhong
,
S.
, and
Zhang
,
X.
,
2021
, “
On the Efficient Modeling of Generic Source Directivity in Gaussian Beam Tracing
,”
J. Acoust. Soc. Am.
,
149
(
4
), pp.
2743
2751
.
10.
Bian
,
H.
,
Tan
,
Q.
,
Zhong
,
S.
, and
Zhang
,
X.
,
2021
, “
Assessment of UAM and Drone Noise Impact on the Environment Based on Virtual Flights
,”
Aerosp. Scie. Technol.
,
118
(
7553
), p.
106996
.
11.
Jiang
,
H.
,
Zhong
,
S.
,
Zhang
,
X.
, and
Huang
,
X.
,
2021
, “
Efficient Storage and Interpolation of Acoustic Transfer Functions
,”
Eng. Anal. Bound. Elem.
,
124
(
5
), pp.
259
265
.
12.
Eller
,
D.
, and
Carlsson
,
M.
,
2003
, “
An Efficient Aerodynamic Boundary Element Method for Aeroelastic Simulations and Its Experimental Validation
,”
Aerosp. Sci. Technol.
,
7
(
7
), pp.
532
539
.
13.
Saad
,
Y.
, and
Schultz
,
M. H.
,
1986
, “
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
,”
SIAM J. Sci. Stat. Comput.
,
7
(
3
), pp.
856
869
.
14.
Shen
,
L.
, and
Liu
,
Y.
,
2007
, “
An Adaptive Fast Multipole Boundary Element Method for Three-Dimensional Acoustic Wave Problems Based on the Burton–Miller Formulation
,”
Comput. Mech.
,
40
(
3
), pp.
461
472
.
15.
Greengard
,
L.
, and
Rokhlin
,
V.
,
1987
, “
A Fast Algorithm for Particle Simulations
,”
J. Comput. Phys.
,
73
(
2
), pp.
325
348
.
16.
Rokhlin
,
V.
,
1988
, “
A Fast Algorithm for the Discrete Laplace Transformation
,”
J. Complex.
,
4
(
1
), pp.
12
32
.
17.
Hackbusch
,
W.
,
1999
, “
A Sparse Matrix Arithmetic Based on H-Matrices. Part I: Introduction to H-Matrices
,”
Computing
,
62
(
2
), pp.
89
108
.
18.
Brunner
,
D.
,
Junge
,
M.
,
Rapp
,
P.
,
Bebendorf
,
M.
, and
Gaul
,
L.
,
2010
, “
Comparison of the Fast Multipole Method With Hierarchical Matrices for the Helmholtz-Bem
,”
Comput. Model. Eng. Sci. (CMES)
,
58
(
2
), pp.
131
160
.
19.
Zheng
,
C.-J.
,
Chen
,
H.-B.
,
Gao
,
H.-F.
, and
Du
,
L.
,
2015
, “
Is the Burton–Miller Formulation Really Free of Fictitious Eigenfrequencies?
,”
Eng. Anal. Bound. Elem.
,
59
, pp.
43
51
.
20.
Schenck
,
H. A.
,
1968
, “
Improved Integral Formulation for Acoustic Radiation Problems
,”
J. Acoust. Soc. Am.
,
44
(
1
), pp.
41
58
.
21.
Kirkup
,
S. M.
,
2007
,
The Boundary Element Method in Acoustics
,
Integrated Sound Software
,
Hebden Bridge
.
22.
Burton
,
A.
, and
Miller
,
G.
,
1971
, “
The Application of Integral Equation Methods to the Numerical Solution of Some Exterior Boundary-Value Problems
,”
Proc. R. Soc. Lond. A. Math. Phys. Sci.
,
323
(
1553
), pp.
201
210
.
23.
Amini
,
S.
, and
Harris
,
P.
,
1990
, “
A Comparison Between Various Boundary Integral Formulations of the Exterior Acoustic Problem
,”
Comput. Methods. Appl. Mech. Eng.
,
84
(
1
), pp.
59
75
.
24.
Marburg
,
S.
,
2016
, “
The Burton and Miller Method: Unlocking Another Mystery of Its Coupling Parameter
,”
J. Comput. Acoust.
,
24
(
1
), p.
1550016
.
25.
Chapman
,
C.
,
1990
, “
The Spiral Green Function in Acoustics and Electromagnetism
,”
Proc. R. Soc. Lond. Ser.A: Math. Phys. Sci.
,
431
(
1881
), pp.
157
167
.
26.
Chapman
,
C.
,
1993
, “
The Structure of Rotating Sound Fields
,”
Proc. R. Soc. Lond. Ser. A: Math. Phys. Sci.
,
440
(
1909
), pp.
257
271
.
27.
Dunn
,
M.
,
Tweed
,
J.
, and
Farassat
,
F.
,
1999
, “
The Application of a Boundary Integral Equation Method to the Prediction of Ducted Fan Engine Noise
,”
J. Sound. Vib.
,
227
(
5
), pp.
1019
1048
.
28.
Choi
,
H.-L.
, and
Lee
,
D. J.
,
2006
, “
Development of the Numerical Method for Calculating Sound Radiation From a Rotating Dipole Source in an Opened Thin Duct
,”
J. Sound. Vib.
,
295
(
3–5
), pp.
739
752
.
29.
Ylä-Oijala
,
P.
, and
Järvenpää
,
S.
,
2006
, “
Iterative Solution of High-Order Boundary Element Method for Acoustic Impedance Boundary Value Problems
,”
J. Sound. Vib.
,
291
(
3–5
), pp.
824
843
.
30.
Hackbusch
,
W.
, and
Khoromskij
,
B. N.
,
2000
, “
A Sparse H-Matrix Arithmetic. Part II: Application to Multi-Dimensional Problems
,”
Computing
,
64
(
1
), pp.
21
47
.
31.
Goreinov
,
S. A.
,
Tyrtyshnikov
,
E. E.
, and
Zamarashkin
,
N. L.
,
1997
, “
A Theory of Pseudoskeleton Approximations
,”
Linear Algebra Appl.
,
261
(
1–3
), pp.
1
21
.
32.
Börm
,
S.
, and
Grasedyck
,
L.
,
2005
, “
Hybrid Cross Approximation of Integral Operators
,”
Numer. Math.
,
101
(
2
), pp.
221
249
.
33.
Bebendorf
,
M.
,
2000
, “
Approximation of Boundary Element Matrices
,”
Numer. Math.
,
86
, pp.
565
589
.
34.
Bebendorf
,
M.
, and
Rjasanow
,
S.
,
2003
, “
Adaptive Low-Rank Approximation of Collocation Matrices
,”
Computing
,
70
(
1
), pp.
1
24
.
35.
Althoen
,
S. C.
, and
Mclaughlin
,
R.
,
1987
, “
Gauss-Jordan Reduction: A Brief History
,”
Amer. Math. Monthly
,
94
(
2
), pp.
130
142
.
36.
Marburg
,
S.
, and
Schneider
,
S.
,
2003
, “
Performance of Iterative Solvers for Acoustic Problems. Part I. Solvers and Effect of Diagonal Preconditioning
,”
Eng. Anal. Bound. Elem.
,
27
(
7
), pp.
727
750
.
37.
Chen
,
J.-T.
,
Lee
,
Y.-T.
, and
Lin
,
Y.-J.
,
2010
, “
Analysis of Mutiple-Shepers Radiation and Scattering Problems by Using a Null-Field Integral Equation Approach
,”
Appl. Acoust.
,
71
(
8
), pp.
690
700
.
38.
Carley
,
M.
,
2006
, “
Series Expansion for the Sound Field of Rotating Sources
,”
J. Acoust. Soc. Amer.
,
120
(
3
), pp.
1252
1256
.
39.
Carley
,
M.
,
2009
, “
Inversion of Spinning Sound Fields
,”
J. Acoust. Soc. Amer.
,
125
(
2
), pp.
690
697
.
40.
Carley
,
M. J.
,
2010
, “
Series Expansion for the Sound Field of a Ring Source
,”
J. Acoust. Soc. Amer.
,
128
(
6
), pp.
3375
3380
.
41.
Jiang
,
H.
,
Zhong
,
S.
,
Wu
,
H.
,
Zhang
,
X.
,
Huang
,
X.
,
Zhou
,
G.
, and
Chen
,
B.
,
2022
, “
Radiation Modes of Propeller Tonal Noise
,”
J. Vib. Acoust.
,
144
(
2
), p.
021009
.
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