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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

Ωr2JmB 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

sinmBb 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

AxJmB +(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.

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