Prediction of the flow and acoustic fields generated by an isolated propeller

Abstract

Propeller-driven aircraft noise has been a problem to passengers and community for decades. With the recent advances and focus on the development of electric propulsion and unmanned aerial vehicles, the noise emitted by propellers is still a concern. The design of low-noise propellers requires a balance between noise emission and aerodynamic performance, which commonly walk in different ways during design. Numerical approaches such computational fluid dynamics (CFD) coupled with noise prediction methods can aid in the design of propellers and in their installation effects. Analytical, semi-empirical or reduced order methods are desired for the design process as their use make possible the analyses of multiple configurations and optimization processes. We propose an analysis and validation of a simulation model for predicting the flow field and aerodynamic characteristics of propellers using the opensource code OpenFOAM. A 4-blade tractor propeller geometry of diameter D = 0.237 m was chosen from the literature. Unsteady Reynolds Averaged Navier-Stokes simulations were conducted using the SST turbulence model. A dynamic mesh approach was adopted to simulate the rotation of the propeller, in which the domain is divided in a static region and a rotating region. Sensitivity to grid refinement and boundary conditions are assessed and results are validated through comparisons with reference data. The acoustic field is obtained by different approaches: acoustic analogies and semi-analytical methods, and the results are compared to other numerical data in the literature. In the first approach the tonal noise field is obtained from the simulated flow field using the Ffowcs-Williams and Hawkings analogy. In the second approach, the distributed thrust and torque coefficients, obtained via CFD, are used as input to semi-analytical methods for the prediction of the thickness and loading components of propeller noise. Results of both approaches are compared in terms of accuracy and computational cost.

Full text

Prediction of the flow and acoustic fields generated by an isolated
propeller
da Silva, F. D.1; Batista, P. A.1; Xavier, G. H.1; Chadlvski, J. V. V. M.1
1TEG-Thermodfluids Engineering Group, Universidade Federal de Santa Catarina, Joinville, SC, Brazil, filipe.dutra@teg.ufsc.br
Abstract
Propeller-driven aircraft noise has been a problem to passengers and community for decades. With the recent
advances and focus on the development of electric propulsion and unmanned aerial vehicles, the noise emitted by
propellers is still a concern. The design of low-noise propellers requires a balance between noise emission and
aerodynamic performance, which commonly walk in different ways during design. Numerical approaches such
computational fluid dynamics (CFD) coupled with noise prediction methods can aid in the design of propellers
and in their installation effects. Analytical, semi-empirical or reduced order methods are desired for the design
process as their use make possible the analyses of multiple configurations and optimization processes. We propose
an analysis and validation of a simulation model for predicting the flow field and aerodynamic characteristics of
propellers using the opensource code OpenFOAM. A 4-blade tractor propeller geometry of diameter D = 0.237
m was chosen from the literature. Unsteady Reynolds Averaged Navier-Stokes simulations were conducted using
the SST turbulence model. A dynamic mesh approach was adopted to simulate the rotation of the propeller, in
which the domain is divided in a static region and a rotating region. Results are validated through comparisons
with reference data. The acoustic field is obtained by different approaches: acoustic analogies and semi-analytical
methods, and the results are compared to other numerical data in the literature. In the first approach the tonal noise
field is obtained from the simulated flow field using the Ffowcs-Williams and Hawkings analogy. In the second
approach, the distributed thrust and torque coefficients, obtained via CFD, are used as input to analytical methods
for the prediction of the thickness and loading components of propeller noise. Results of both approaches are
compared and discussed.
Keywords: Propeller Noise, OpenFOAM, Semi-analytical Methods.
PACS: 43.28.-g; 43.28.Ra; 43.50.Nm.
FIA 2020/22
XII CONGRESSO/CONGRESO IBEROAMERICANO DE ACÚSTICA
XXIX ENCONTRO DA SOCIEDADE BRASILEIRA DE ACÚSTICA - SOBRAC
Florianópolis, SC, Brasil

2Prediction of the flow and acoustic fields generated by an isolated propeller FIA 2020/22 | XXIX Sobrac
1. INTRODUCTION
Propeller noise is a main concern in turboprop
aircraft, as well as, vertical take-off and landing
(VTOL) vehicles. With the recent advances and
focus on the development of electric propulsion
and unmanned aerial vehicles (UAVs), the noise
emitted by propellers is still a concern. The de-
sign of low-noise propellers requires a balance
between noise emission and aerodynamic perfor-
mance, which commonly walk in different ways
during design [1].
Numerical approaches such computational fluid
dynamics (CFD) coupled with noise prediction
methods can aid in the design of propellers and
in their installation effects. Large-eddy simu-
lation (LES) is a high-fidelity alternative that
makes possible the deeper analyses of the phe-
nomena. On the other hand, the use of hybrid
approaches [
2
,
3
] as well as unsteady Reynolds
Averaged Navier-Stokes (RANS) simulations [
4
–
9
] can lead to reasonable results with reduced
computational cost. Analytical, semi-empirical
and reduced order methods are desired for the de-
sign process as their use make possible the anal-
yses of multiple configurations and optimization
processes.
When dealing with noise prediction from turbu-
lent flows, different methods can be used. Direct
methods perform the noise computation in the
same domain as the fluid dynamics, without any
modeling for the sound. The full set of equa-
tions, Navier-Stokes or Euler, is solved in the
domain of interest for both the flow and acoustic
fields. This requires a domain sufficiently large
in order to calculate noise propagation up to the
receptor points. Due to the difficulties of using
direct methods, the so called hybrid approaches
are commonly used. In such methods, sound-
generation due to aerodynamics is treated sepa-
rately from the acoustic transport process. The
sound field is computed, with the flow field as in-
put, by using acoustic analogies such as Ffowcs
Williams and Hawkings [
10
]. An alternative is to
use semi-empirical methods to model the sources
of noise. For the propeller case, some methods
use thrust and torque distributions to estimate
the tonal noise [
11
–
14
]. When dealing with such
methods, CFD can be used both to generate input
data [
15
] as well as provide source-field infor-
mation to be used for the adjustment of model
parameters.
We propose an analysis of different approaches
to predict the acoustic field froam an isolated pro-
peller. Our objective is to develop and validate
a simulation model, based on the opensource
code OpenFOAM, to predict the aerodynamic
characteristics and acoustic fields of propellers.
Unsteady RANS simulation are conducted using
the SST model [
16
] to solve the flow field over a
four-blade propeller. The results of the simula-
tion are used to obtain the acoustic field both by
an acoustic analogy approach and by analytical
prediction methods.
2. METHODS
This section describes the geometry, computa-
tional domain and mesh and the models used for
noise computation.
2.1 Geometry and Experimental Data
A 4-blade tractor propeller geometry of diameter
D=0.237
m was used (Fig. 1). Details of the
geometry and descriptions of the measurements
carried out in the Low Speed Low Turbulence
Wind Tunnel (LTT) of Delft University of Tech-
nology can be found in de Vries et al. [
17
], Sin-
nige et al. [
18
]. For the present analysis, only
the isolated propeller will be considered. Ex-
perimental data such as thrust coefficients are
available in de Vries et al. [
17
], Sinnige et al.
[
18
] and will be used for validation. On the other
hand, the validation of the computed sound field
will be provided by comparisons with the very
large eddy simulation (VLES) based on the lat-
tice Boltzmann method (LBM) from Avallone
et al. [
19
] for a pylon-mounted installed pro-
peller. Data was extracted from the references
using the WebPlotDigitizer tool [20].
2.2 Numerical model
Incompressible, unsteady Reynolds Averaged
Navier-Stokes (URANS) simulations were con-
ducted using the SST turbulence model [
16
] im-
plemented in OpenFOAM v2012 [
21
]. The sim-
ulations used a dynamic mesh approach to sim-
ulate the rotation of the propeller, in which the

FIA 2020/22 | XXIX Sobrac Prediction of the flow and acoustic fields generated by an isolated propeller 3
Figure 1: Image of the propeller geometry studied by
Sinnige et al. [18]
domain is divided in a static region and a rotating
region, coupled by and arbitrary mesh interface
(AMI). The computational domain and boundary
conditions are depicted in Fig. 2. The baseline
cylindrical domain has a diameter of
8D
, where
D
is the propeller diameter. It extends
3D
up-
stream and 7Ddownstream of the propeller.
A freestream inflow/outflow condition was im-
posed in the upstream and lateral boundary of the
domain. A freestream velocity of
V0=40
m/s
was imposed with ambient pressure. For com-
puting turbulence quantities, a low turbulence
wind tunnel condition was considered, with tur-
bulence intensity
I=0.1%
and
νt/ν=5
. For the
outflow, a zero-gradient condition was used for
velocity and turbulence quantities, with ambient
back pressure. On the propeller, a no-slip condi-
tion with standard wall functions was used. At
the interface between the static and rotating do-
mains, a Cyclic Arbitrary Mesh Interface (AMI)
condition was applied. The rotation frequency
(
n
) was calculated to obtain an advance ratio of
J=V0/nD =0.8.
The computational unstructured grid of
5.45 ×
106
volumes was generated using the code SA-
LOME [
22
]. The grid is formed predominantly
tetrahedral volumes and is depicted in Figure 3.
Near the walls, layers of prismatic elements were
created in order to correctly solve the boundary
layers, as depicted in Figure 4. Finally, the mesh
on the surface of the propeller is shown in Fig-
ure 5.
The simulation was initialized with an uniform
flow field of
V0
. First order numerical were used
in the initial timesteps and were switched to sec-
ond order numerical schemes during the devel-
0.6D
8D
3D 7D
x
y
Freestream Outflow
wall
AMI
z
1.7D
Figure 2: Computational domain and boundary
conditions
opment of the flow. For the convective terms,
linear upwind and limited linear schemes were
used for velocity and turbulence, whereas a Mul-
tidirectional limited linear scheme was adopted
for the gradient terms. Time discreization was
based on an implicit Crank-Nicolson scheme.
For the pressure-velocity coupling, the PIMPLE
algorithm was used (see Holzmann [
23
]). The
simulation time is equivalent to
30
complete rev-
olutions with approximately
1000
time-steps per
revolution.
2.3 Noise computation - CFD
For the far-field noise computations we used a
dynamic library called libAcoustics, which is in-
tegrated with OpenFOAM and was developed
by Epikhin et al. [
24
] and llya Evdokimov et al.
[
25
]. This code contains acoustic analogies to
be used in conjunction with CFD computations.
Validation of the library has been previously ad-
dressed by [24,26–28].
In this work, the Ffwocs-Willians and Hakings
analogy (FW-H) [
10
] based on permeable sur-
faces was used to compute the far-field noise. In
such approach, near field pressure and velocity
data are stored on an arbitrary control surface,
which should encompass the most significant
sound-generating regions. This surface infor-
mation is used as an input for the far-field noise
computations. Particularly the Garrick Triangle
(GT) formulation, described by Brès et al. [
29
],
was used as it shows increased computational
efficiency for wind tunnel configurations.

4Prediction of the flow and acoustic fields generated by an isolated propeller FIA 2020/22 | XXIX Sobrac
Figure 3: XY-plane slice of the computational mesh. The red-shaded area represents the FWH surface.
Figure 4: Image of the mesh close to the hub-blade
junction.
Two different FWH surfaces were used. The
surfaces are three-dimensional and have a cylin-
drical shape as shown in Figure 3, in red. Surface
1 (S1) has a diameter of
1.05D
and extends ax-
ially from
x=−0.85D
to
x=4.2D
. Surface 2
(S2) has the same diameter, extending, however,
from x=−1.1Dto x=5.5D.
Data were recorded on the FWH surfaces dur-
Figure 5: Mesh on the surface of the propeller.
ing
13.5
revolutions, with approximately
1880
timesteps per revolution, resulting in a sampling
frequency of
400
kHz. The sound field was cal-
culated on an arc of radius
2D
, consisting of
thirty-eight microphone positions, following the
polar angle convention shown in Figure 6. The
noise Power Spectral Density (PSD) spectrum
was obtained by the [
30
] method with resulting
frequency resolution of
42
Hz. A Hanning win-
dow was employed with an overlap of
75%
be-
tween blocks. In order to compare with the ref-
erence data, the PSD was converted to Sound
Pressure Level (SPL) in 1/12-octave bands.

FIA 2020/22 | XXIX Sobrac Prediction of the flow and acoustic fields generated by an isolated propeller 5
2.4 Analytical noise prediction
Two analytical methods were selected for the
tonal noise prediction. The first one unites the
loading noise theory from Gutin [
12
] with the
thickness noise method form Deming [
13
]. We
implemented the far-field equations as presented
by Kotwicz Herniczek et al. [
11
]. The loading
noise is computed as,
P
mL=mBΩ
2√2πcS Zti p
hub dT
dr cosϕ−dQ
dr
c
Ωr2JmB dr
(1)
where
P
mL
[Pa] is the rms of the loading noise
pressure,
m
is the number of the harmonic,
B
is
the number of blades,
Ω
[rad/s] is the rotational
speed,
c
[m/s] is the speed of sound,
r
[m] is
the local radial position on the blade,
S
is the
observer radial position,
ϕ
[rad] is the observer
polar angle,
dR/dr
[N/m] is the elemental trust,
dQ/dr
[N.m/m] is the elemental torque and
JmB
is the Bessel function (see eq.3).
The thickness noise equations is defined as fol-
lows,
P
mT=−ρ(mBΩ)2B
3√2πSZti p
hub
bhJmB dr (2)
where,
P
mT
[Pa] is the rms amplitude of the thick-
ness noise,
ρ
[kg/
m3
] is the fluid density,
b
[m]
is the local airfoil chord and
t
[m] is the local
maximum airfoil thickness.
JmB =JmB mBΩ
crsinϕ(3)
The second method is the one originally pro-
posed by Barry and Magliozzi [
14
], which takes
into account the effects of forward flight and the
blade twist angle. We implemented the modified
version of the far-field formulation presented by
Kotwicz Herniczek et al. [
11
]. The loading noise
component is computed with the following equa-
tion,
P
mL=1
√2πS0Zti p
hub
r
bcosφt
sinmBb cos φt
2r
(M+X/S0)Ω
c(1−M2)
dT
dr −1
r2
dQ
dr (4)
JmB +(1−M2)Y r
2S2
0
(JmB−1−JmB+1)dr
where
X
[m] is the axial position of the observer
as shown in Figure 6,
Y
[m] is the distance of
the observer to the propeller axis,
M
is the free-
stream Mach number, S0=pX2+ (1−M2)Y2
is the amplitude radius,
φt
is the local blade twist
angle and
JmB
is the Bessel function shown in
equation 3. Thickness noise is computed by the
following equation,
P
mT=−ρm2Ω2B3
2√2π(1−M2)2
(S0+MX )2
S3
0
(5)
Zti p
hub
AxJmB +(1−M2)Y r
2S2
0
(JmB−1−JmB+1)dr
where
Ax
is the local airfoil cross-sectional area,
which is approximated by 0.6853bh [m2].
JmB =JmB mBΩY r
cS0(6)
The necessary geometric input parameters were
obtained from Sinnige et al. [
18
] and the thrust
and torque distributions were taken from the
CFD. To do so, each blade was divided in
26
segments of
∆r=0.033R
, where
R=D/2
is the
blade-tip radius. For each segment, the axial
force and moment components were calculate by
integration of pressure and wall shear stress. The
segment trust (
∆T
) and torque (
∆Q
) was divided
by
∆r
to approximate
dT /dr
and
dQ/dr
of each
segment.
3. RESULTS
In this section, the aerodynamic and acoustic
results are presented and discussed.

6Prediction of the flow and acoustic fields generated by an isolated propeller FIA 2020/22 | XXIX Sobrac
Mic
Propeller
X
S
Y
Flow direction
𝜃 = 180° − 𝜑
𝜑
Figure 6: Microphone positions considering different
coordinate systems. Black - Gutin [12] and Deming
[
13
] model, Blue - Barry and Magliozzi [
14
] model and
Green - CFD.
3.1 Aerodynamic Results
Table 1show the obtained thrust and torque coef-
ficients. The thrust coefficient is compared to the
experimental result from de Vries et al. [
17
] and
to the numerical data from Avallone et al. [
3
].
Our numerical simulations underpredicted the ex-
perimental thrust coefficient by about
11%
and
deviates by about
3%
from LBM results from
Avallone et al. [
3
]. In spite of the deviations
from the measurements, considering that we sim-
ulated the isolated propeller instead of the whole
apparatus, the results are consistent with the lit-
erature.
Table 1: Comparison of aerodynamic coefficients of
thrust and torque
Present Exp. - [17] Num.- [3]
ct0.0842 0.095 0.087
cq0.0167 - -
Figure 7presents the distributions of thrust
and torque coefficients as function of the non-
dimensional radial position along the blade
ξ=
r
R. The distribution were obtained following the
procedure described in Subsection 2.4. As men-
tioned, these results are used as input data for
both noise prediction models.
3.2 Acoustic Results - OpenFOAM
The comparison of SPL spectra obtained from
both FWH surfaces, for different directivity an-
gles, is depicted in Figure 8. Each plot presents
0.2 0.4 0.6 0.8 1
-1
0
1
2
3
4
ξ=r/R
dct/dξ
(a)
0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
ξ=r/R
dcq/dξ
(b)
Figure 7: Radial distribution of elemental thrust (a) and
torque (b) coefficients.
the spectra considering postive angles, denoted
by
+θ
, and negative angles, denoted by
−θ
. Re-
garding the blade passing frequency (BPF), re-
sults computed from different surfaces are very
similar. However, for the second harmonic, in
some observer positions, not only there are sig-
nificant differences between S1 and S2, but also
the peak levels differ significantly between posi-
tive and negative angles. This is an inconsistent
result, since the problem should be symmetric.
It is not clear what caused these disparities in the
second peak. They could be caused by spurious
effect of the wake crossing the surfaces or errors
induced by asymmetries of the tetrahedral mesh.
Further studies of grid refinement and shape o
the FWH surface should be addressed. Neverthe-
less, these effects do not significantly affect the
peak levels of the first BPF for the considered
directivity range. As show in Figure 9, minor

FIA 2020/22 | XXIX Sobrac Prediction of the flow and acoustic fields generated by an isolated propeller 7
100
20
30
40
50
60
70
80
90
SPL(dB)
f/BPF
S1 +θ
S2 +θ
S1 −θ
S2 −θ
(a) θ=±60◦
100
20
30
40
50
60
70
80
90
SPL(dB)
f/BPF
S1 +θ
S2 +θ
S1 −θ
S2 −θ
(b) θ=±90◦
100
20
30
40
50
60
70
80
90
SPL(dB)
f/BPF
S1 +θ
S2 +θ
S1 −θ
S2 −θ
(c) θ=±120◦
100
20
30
40
50
60
70
80
90
SPL(dB)
f/BPF
S1 +θ
S2 +θ
S1 −θ
S2 −θ
(d) θ=±150◦
Figure 8: Comparison of SPL spectra computed from different surfaces.
differences can be noted between results from
different surfaces in positive and negative angles.
For the subsequent analyses only surface S2 was
used.
Figure 10 depicts the comparison between SPL
spectra in 1/12-octave bands obtained via URAN-
S/FWH with those obtained from LBM by Aval-
lone et al. [
3
]. Is important to emphasize that
Avallone et al. [
3
] considered an pylon-mounted
installed propeller, thus we included spectra for
microphones in the retreating and advancing
blade sides of the pylon. Due to the nature of
URANS modeling, we do not expect to predict
the broadband sources and our comparison will
be limited to tonal levels. At
θ=75◦
(Figure 10)
the level of the first harmonic differs by about
5.5
dB between the URANS and LBM. At
θ=100◦
the differences are about
6
dB with respect to the
60 80 100 120 140 160
50
55
60
65
70
75
80
85
SPL(dB)
θ [°]
S1 +θ
S1 −θ
S2 +θ
S2 −θ
Figure 9: SPL at the BPF computed from different
surfaces at different directivity angles.
advancing-blade side and
1.5
dB with respect to
the retreating-blade side. Differences are higher
than 8 dB for the second harmonic.

8Prediction of the flow and acoustic fields generated by an isolated propeller FIA 2020/22 | XXIX Sobrac
100101
30
40
50
60
70
80
f/BPF
SPL[dB]
Num. +θ
Num. −θ
Avallone et al. (2018) − adv
Avallone et al. (2018) − ret
(a) θ=±75◦
100101
30
40
50
60
70
80
f/BPF
SPL[dB]
(b) θ=±100◦
Figure 10: Comparison of SPL spectra in 1/12 octave
bands with those from Avallone et al. [3]
Even though the comparison between the differ-
ent simulations is inconclusive, since we com-
pare and isolated propeller with an installed one,
results for the BPF tone are consistent with the
reference high-fidelity simulations. Compar-
isons with experimental data are required to as-
sess the real accuracy of the modeling and will
be addressed in future studies.
3.3 Acoustic Results - Semi-analytical
The results from the tonal noise prediction mod-
els are presented in Figure 11 considering only
the blade-passing frequency. In Figure 11(a), re-
sults from the Gutin [
12
] and Deming [
13
] model
(GD) are presented, considering the total noise,
as well as the individual contributions of load-
ing and thickness noise. The predictions from
the CFD/FWH simulations are used as basis of
comparison. The differences between the total
SPL and CFD results vary from 1dB at θ=60◦
to 8dB at θ=150◦.
Figure 11(b) depicts results for Barry and
Magliozzi [
14
] model (BM). In this case, the dif-
ferences between the semi-analytical and CFD
results vary from
3
dB at
θ=60◦
to
14
dB at
θ=150◦
. When comparing both the total SPL
from both models, those from the GD model
were closer to the CFD/FWH predictions. Nev-
ertheless, both models failed to reproduce the
directivity trend.
By looking at the individual contributions of
loading and thickness noise, we can note that
the loading noise models were capable of repro-
ducing the directivity from the CFD predictions.
Also it suggestive that an overprediction of the
thickness component by the analytical models
may be the responsible for the overestimation
of the total SPL. It is important to mention that
errors might be present since we are using the
far-field version of the equations to predict noise
at a radial distance of 2D.
4. CONCLUSIONS
We presented a simulation model to predict tonal
noise and aerodynamic characteristics of isolated
propellers using opensource tools. In general,
aerodynamic and acoustics results in reasonable
agreement with experimental and numerical data
in the literature. Tonal noise results for the blade-
passing frequency did not show significant sensi-
tivity to the size of the FWH surfaces.
Predictions from the analytical models showed
higher tonal noise levels at the BPF in compar-
ison to the CFD predictions. The reason for
these disparities are possibly due to an overpre-
diction of the thickness noise component by the
employed methods. Nevertheless the computa-
tional cost of such models is significantly lower,
specially if coupled with analytical approaches,
e.g. blade element momentum theory, for the
estimation of thrust and toque distributions.
Future works will be directed to improve the sim-
ulation model by performing sensitivity tests to
grid refinement. Comparisons with experimental
results will be performed to assess the accuracy
of the CFD simulations. In addition, more effort
will be directed to understand the errors of the
analytical approach.

FIA 2020/22 | XXIX Sobrac Prediction of the flow and acoustic fields generated by an isolated propeller 9
40 60 80 100 120 140
40
50
60
70
80
90
θ [o]
SPL [dB]
GD - Total
GD - thickness
GD - loading
CFD
(a) Gutin [12] and Deming [13]
40 60 80 100 120 140
40
50
60
70
80
90
θ [o]
SPL [dB]
BM - Total
BM - thickness
BM - loading
CFD
(b) Barry and Magliozzi [14]
40 60 80 100 120 140
40
50
60
70
80
90
θ[o]
SPL [dB]
CFD
Gutin and Deming
Barry and Magliozzi
(c) Both models
Figure 11: Predictions of the tonal SPL at the BPF
through different modeling approaches.
5. ACKNOWLEDGMENTS
The authors acknowledge Dr. Thomas Sinnige
for providing the propeller geometry. Simula-
tion were conducted using the computational
resources from LabCC- Laboratório de com-
putação científica, CTJ-UFSC.
REFERENCES
[1]
Ohad Gur and Aviv Rosen. Design of Quiet Propeller
for an Electric Mini Unmanned Air Vehicle. Journal
of Propulsion and Power, 25(3):717–728, May 2009.
ISSN 0748-4658, 1533-3876. doi:10.2514/1.38814.
[2]
Samuel Afari, Reda R. Mankbadi, and Vladimir V.
Golubev. Towards High-fidelity Analysis of Noise
Radiation and Control of Propeller-driven UAV. In
25th AIAA/CEAS Aeroacoustics Conference, Delft,
The Netherlands, May 2019. American Institute of
Aeronautics and Astronautics. ISBN 978-1-62410-
588-3. doi:10.2514/6.2019-2632.
[3]
Francesco Avallone, Damiano Casalino, and Daniele
Ragni. Impingement of a propeller-slipstream
on a leading edge with a flow-permeable insert:
A computational aeroacoustic study. Interna-
tional Journal of Aeroacoustics, 17(6-8):687–711,
November 2018. ISSN 1475-472X, 2048-4003.
doi:10.1177/1475472X18788961.
[4]
Giulia Chirico, George N Barakos, George Barakos,
Nicholas Bown, and Nicholas Bown. COMPUTA-
TIONAL AEROACOUSTIC ANALYSIS OF PRO-
PELLER INSTALLATION EFFECTS. page 18,
2017.
[5]
Jason Hambrey. Computational Aeroacoustic Pre-
diction of Propeller Noise Using Grid-Based and
Grid-Free CFD Methods. Master of Applied Sci-
ence, Carleton University, Ottawa, Ontario, 2017.
[6]
Nabil Ben Nasr, Fabrice Falissard, Julien Decours,
Robert Gaveriaux, Yves Delrieux, Sylvette Canard-
Caruana, Martin Laban, Harry Brouwer, Martin Al-
breicht, Christian Scholz, Christophe Diette, and
Didier Chartrain. Propeller Analysis Using Low
& High Fidelity Aero-acoustic Methods. In 35th
AIAA Applied Aerodynamics Conference, Denver,
Colorado, June 2017. American Institute of Aero-
nautics and Astronautics. ISBN 978-1-62410-501-2.
doi:10.2514/6.2017-3573.
[7]
Nando v. Arnhem, Tomas Sinnige, Tom C. Stokker-
mans, Georg Eitelberg, and Leo L. Veldhuis. Aero-
dynamic Interaction Effects of Tip-Mounted Pro-
pellers Installed on the Horizontal Tailplane. In
2018 AIAA Aerospace Sciences Meeting, Kissimmee,
Florida, January 2018. American Institute of Aero-
nautics and Astronautics. ISBN 978-1-62410-524-1.
doi:10.2514/6.2018-2052.
[8]
Tom C. Stokkermans, Sebastiaan Nootebos, and
Leo L. Veldhuis. Analysis and Design of a Small-
Scale Wingtip-Mounted Pusher Propeller. In AIAA
Aviation 2019 Forum, Dallas, Texas, June 2019.
American Institute of Aeronautics and Astronau-
tics. ISBN 978-1-62410-589-0. doi:10.2514/6.2019-
3693.
[9]
Hugo F. Bento, Reynard de Vries, and Leo L.
Veldhuis. Aerodynamic Performance and Inter-
action Effects of Circular and Square Ducted Pro-
pellers. In AIAA Scitech 2020 Forum, Orlando,

10 Prediction of the flow and acoustic fields generated by an isolated propeller FIA 2020/22 | XXIX Sobrac
FL, January 2020. American Institute of Aeronau-
tics and Astronautics. ISBN 978-1-62410-595-1.
doi:10.2514/6.2020-1029.
[10]
J. E. Ffowcs Williams and D. L. Hawkings. Sound
generation by turbulence and surfaces in arbitrary
motion. Philosophical Transactions of the Royal
Society of London. Series A, Mathematical and Phys-
ical Sciences, 264(1151):321–342, May 1969. ISSN
00804614.
[11]
Mark T. Kotwicz Herniczek, Daniel Feszty, Sid-Ali
Meslioui, Jong Park, and Fred Nitzsche. Evalua-
tion of Acoustic Frequency Methods for the Predic-
tion of Propeller Noise. AIAA Journal, 57(6):2465–
2478, June 2019. ISSN 0001-1452, 1533-385X.
doi:10.2514/1.J056658.
[12]
L. Gutin. On the sound field of a rotating propeller.
Technical Report NACA-TM-1195, National Advi-
sory Committee for Aeronautics, Washington,DC,
October 1948.
[13]
A. M. Deming. Noise from propellers with symmet-
rical sections at zero blade angle ii. Technical Report
NACA-TM-679, National Advisory Committee for
Aeronautics, Washington, DC, December 1938.
[14]
Frank W. Barry and Bernard Magliozzi. Noise
detectability prediction method for low tip speed pro-
pellers. Technical Report AD0729432, UNITED
TECHNOLOGIES CORP HAMILTON STAN-
DARD DIV, WINDSOR LOCKS, CT, 06 1971.
[15]
Jatinder Goyal, Tomas Sinnige, Francesco Avallone,
and Carlos Ferreira. Aerodynamic and Aeroacoustic
Characteristics of an Isolated Propeller at Positive
and Negative Thrust. doi:10.2514/6.2021-2187.
[16]
F. R. Menter. Two-equation eddy-viscosity
turbulence models for engineering applica-
tions. AIAA Journal, 32(8):1598–1605, 1994.
doi:10.2514/3.12149.
[17]
Reynard de Vries, Tomas Sinnige, Biagio
Della Corte, Francesco Avallone, Daniele Ragni,
Georg Eitelberg, and Leo L. Veldhuis. Tractor
Propeller-Pylon Interaction, Part I: Characteriza-
tion of Unsteady Pylon Loading. In 55th AIAA
Aerospace Sciences Meeting, Grapevine, Texas,
January 2017. American Institute of Aeronautics
and Astronautics. ISBN 978-1-62410-447-3.
doi:10.2514/6.2017-1175.
[18]
Tomas Sinnige, Reynard de Vries, Biagio Della
Corte, Francesco Avallone, Daniele Ragni, Georg
Eitelberg, and Leo L. M. Veldhuis. Unsteady Pylon
Loading Caused by Propeller-Slipstream Impinge-
ment for Tip-Mounted Propellers. Journal of Air-
craft, 55(4):1605–1618, July 2018. ISSN 0021-8669,
1533-3868. doi:10.2514/1.C034696.
[19]
Francesco Avallone, Damiano Casalino, and Daniele
Ragni. Unsteady coherent surface-pressure fluctua-
tions from time-averaged flow data with given two-
point statistics. In 2018 AIAA/CEAS Aeroacoustics
Conference, Atlanta, Georgia, June 2018. American
Institute of Aeronautics and Astronautics. ISBN
978-1-62410-560-9. doi:10.2514/6.2018-4097.
[20]
Ankit Rohatgi. Webplotdigitizer: Version 4.5, 2021.
URL https://automeris.io/WebPlotDigitizer.
[21]
OpenCFD. Openfoam: the open source
cfd toolbox user guide. OpenCFD Ltd,
https://www.openfoam.com/documentation/overview.
Accessed 17 June 2021, 2020.
[22]
SALOME. Salome v9.8 user guide. docs.salome-
platform.org/latest/main/index.html Accessed 20
June 2022, 2021.
[23]
Tobias Holzmann. Mathematics, Numerics, Deriva-
tions and OpenFOAM®. 11 2019.
[24]
A Epikhin, I Evdokimov, M Kraposhin, M Kalugin,
and S Strijhak. Development of a dynamic library for
computational aeroacoustics applications using the
openfoam open source package. Procedia Computer
Science, 66:150–157, 2015.
[25]
llya Evdokimov, UniCFD, and Andrey
Epikhin. unicfdlab/libacoustics: Openfoam+
v1912 version of libacoustics. Jun 2020.
doi:10.5281/zenodo.3878439.
[26]
Andrey Epikhin. Validation of the developed open
source library for far-field noise prediction. In
Proceedings of the 27th International Congress on
Sound and Vibration, Denver, Colorado, July 2021.
Silesian University Press. ISBN 9788378807995.
[27]
Julio Victor Vieira Martins Chadlvski and Filipe Du-
tra da Silva. Prediction of aerodynamic noise gener-
ated by cylinders in uniform flow using openfoaml
aeroacoustics. In Proceedings of the 26th Interna-
tional Congress of Mechanical Engineering, 2021.
doi:10.26678/ABCM.COBEM2021.COB2021-
1128.
[28]
Saman Salehian and Reda Mankbadi. Jet noise
in airframe integration and shielding. Ap-
plied Sciences, 10(2), 2020. ISSN 2076-3417.
doi:10.3390/app10020511.
[29]
G A Brès, F Pérot, and D Freed. A ffowcs williams-
hawkings solver for lattice-boltzmann based compu-
tational aeroacoustics. In Proceedings of the 16th
AIAA/CEAS Aeroacoustics Conference - AIAA 2010,
Stockholm, 2010.
[30]
P. Welch. The use of fast fourier transform for the
estimation of power spectra: A method based on
time averaging over short, modified periodograms.
IEEE Transactions on Audio and Electroacous-
tics, 15(2):70–73, Jun 1967. ISSN 0018-9278.
doi:10.1109/TAU.1967.1161901.