Open Journal of Fluid Dynamics, 2013, 3, 55-60
http://dx.doi.org/10.4236/ojfd.2013.32A009 Published Online July 2013 (http://www.scirp.org/journal/ojfd)
Aerodynamic Sound Radiated from Two-Dimensional
Airfoil with Local Porous Material
Hiromitsu Hamakawa1, Kazuki Hosokai2, Takaaki Adachi2, Eru Kurihara1
1Oita University, Oita, Japan
2Postgraduate Course, Oita University, Oita, Japan
Received May 28, 2013; revised June 5, 2013; accepted June 12, 2013
Copyright © 2013 Hiromitsu Hamakawa et al. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
In the present paper, the attention is focused on the effect of local porous material on aerodynamic sound radiated from
two-dimensional airfoil. We measured the aerodynamic sound radiated from the airfoil with porous material, tripping
wire and porous plate which are mounted locally on the surface of the airfoils near the leading edge. At the normal air-
foil, discrete frequency noise is clearly observed at small attack angle. However, it is clear that its noise generated from
the airfoil decreased with the local porous material on the surface of pressure side of the airfoil. The porous material is
effective to reduce this noise compared with the others. And the sound absorbing coefficient and the air permeability
were measured for test porous material. The sound absorbing coefficient increased at the high frequency band, and the
air permeability became small for porous materials. As the attack angle increased, the discrete frequency noise was not
generated from the normal airfoil. The broadband noises were almost same for all test airfoils.
Keywords: Aerodynamic Sound; Discrete Frequency Noise; Porous Material; Two-Dimensional Airfoil
1. Introduction
Low noise level is an important sales point of the various
kinds of machines as well as high performance and mini-
aturization. This situation is also applied to fans used, for
example, in air conditioners, ventilators and coolers.
The controlling noise source generated from an axial
flow fan is turbulent noise due to vortex shedding when
the fan is operated near the design point [1,2]. Fukano et
al. have investigated the discrete frequency noise gener-
ated by Karman vortex shedding from a flat plate blade
immersed in a uniform two-dimensional flow field, and
theoretically introduced a formula to predict its sound
pressure level [3].
It is generally known that the tonal noise is generated
from two-dimensional airfoil at certain flow conditions at
a discrete frequency about 30 dB above the background
broadband level. This discrete frequency noise is com-
monly generated from fans, wind-turbines, gliders and
small aircrafts, etc. Many studies have been published on
the characteristics and occurrence mechanisms of this
noise [4-10].
On the other hand, there are many studies to reduce the
aerodynamic noise radiated from the airfoil [11-15]. Fu-
kano et al. also reported that the fan noise decreased by
changing the profile of rotor blade [11]. Polacsek et al.
showed that the wavy-leading-edge of blade was effect-
tive to reduce its noise [12]. Nishimura et al. observed
that the fan noise reduced to affix a fur material around
leading edge on the surface of blade for cooling fan [13].
However, the aerodynamic noise may increase when the
rotational speed of fan increases to supplement the de-
crease of fan performance, although an aerodynamic noi-
se decreases for these methods. Therefore, it is consid-
ered that the reduction of aerodynamic noise by changing
the properties on the surface of the blade, which is not
changing the blade profile, is effective, because the de-
sign of high efficiency is more important for industrial
fans. Akishita et al. [14] and Takeishi et al. [15] have
clarified the acoustic characteristic on the porous surface
and the effect of porous surface on Aeolian tone radiated
from a circular cylinder. However, the specifications of
the porous material on the blade, for example, properties,
hole diameter, thickness and optimum position, etc. are
not clear, although it may be effective to reduce an aero-
dynamic sound without decreasing the performance of
fan.
The purpose of the present study is to clarify the effect
of the local porous material mounted near the leading
C
opyright © 2013 SciRes. OJFD

H. HAMAKAWA ET AL. 56
edge on the surface of airfoil on an aerodynamic sound.
And the characteristics of the air permeability and sound
absorbing coefficient of porous materials are also dis-
cussed.
2. Experimental Apparatus and Procedures
2.1. Measurement of Aerodynamic Sound
Our experiments were performed in a low-noise wind
tunnel, which has been described in detail elsewhere [16].
This wind tunnel was an open-circuit with wing-type
silencers in the diffuser located at the outlet of the blower
and splitter-type silencers at the inlet of the blower. The
test section was placed in the anechoic room, which was
rectangular in shape, and 3 m long, 3 m wide, and 3 m
high. The collector was downstream of the test section.
Noise-absorbing furry materials were attached to the
surface of the collector to reduce the interaction noise
between the open jet and the collector. This collector was
connected to a 3-m-long sound absorbent duct. The
background noise was about 63 dB(A) at a freestream
velocity of 50.0 m/s.
Figure 1 shows a schematic view of the test-section
and test airfoil. The cross section of the nozzle exit was a
0.3-m-wide and 0.3-m-high square. A test airfoil was
installed in the test section 100 mm downstream of the
nozzle exit. The freestream velocity ranged from 5 m/s to
45 m/s at the test section inlet. The Reynolds numbers,
based on the chord length, ℓ, and freestream velocity, U∞,
ranged from 3.1 × 104 to 3.4 × 105. The flow past the
nozzle was uniform, and the drift of the freestream ve-
locity was less than about 0.9%. The freestream turbu-
lence level was less than 0.5% of the freestream velocity.
In addition, no peak of velocity fluctuation spectrum at
the test section without the test airfoil was formed at this
velocity range. Two end plates were placed at the top and
bottom of the test section, and a test airfoil was placed
vertically and rigidly supported between them. These
were 900-mm-wide and 450-mm-long acoustically non-
reflecting end plates, which were large enough to cover
the jet edge region. The downstream distance from the
test airfoil to the edges of the end plates was 350 mm.
Microphone
1000
100 350(=3.5ℓ)
Figure 1. Schematic of test section of wi nd tunne l.
These end plates were composed of a 25-mm-thick poly-
styrene porous material and 25-mm-thick glass wool
backed with a punched steel plate to reinforce the plate
rigidity [16]. It was clearly observed that the results for
the non-reflecting end plates were almost the same as the
attenuation characteristics of the free field.
Figure 2 shows the test airfoils. The porous plate was
mounted near the leading edge on the surface of test air-
foil as shown in Figure 2(a) and was made from a 0.2-
mm-thick plate with many holes of diameter, d0, of about
0.5 mm. The thickness of the background air space is
about 4 mm. The airfoil has NACA0012 profile, the
chord length is 100 mm and span length is 300 mm.
The Styrofoam or Polyethylene foam as porous mate-
rial was mounted near the leading edge on the surface of
test airfoil as shown in Figure 2(b) and was thickness of
about 4 mm. The tripping wire was mounted near the
leading edge on the surface of test airfoil as shown in
Figure 2(c) and was diameter, d, of 2.6 mm or 0.8 mm.
The Polyethylene foam was mounted on the both sur-
faces of test airfoil as shown in Figure 2(d). The normal
airfoil of NACA0012 profile without porous materials
was shown in Figure 2(e). The features and symbols of
test airfoils are presented in Table 1.
The aerodynamic sound in the far field from the test
airfoil was measured at X = 0 mm, Y = 1000 mm, and Z =
0.09ℓ
0.10ℓ
3ℓ
Porous material
(b) (c) (d) (e)(a)
ℓ
(a)
Figure 2. Test airfoils.
Table 1. Experimental materials.
Symbols Feature Figure
Plate Porous plate, d0 = 0.5 mm Figure 2(a)
Material APorous material, Styrofoam Figure 2(b)
Material BPorous material, Polyethylene foam Figure 2(b)
Trip 2.6 Tripping wire, d = 2.6 mm Figure 2(c)
Trip 0.8 Tripping wire, d = 0.8 mm Figure 2(c)
Both SidesMaterial B on the both sides Figure 2(d)
Normal Normal type Figure 2(e)

H. HAMAKAWA ET AL. 57
0 mm using a microphone. When the observation loca-
tion was far enough to be considered as the far field, the
effect of the near field could be neglected. In this meas-
uring position, the near field component attenuates, and
the far field component is about 10 dB larger than the
near field component for phenomena that occur over 170
Hz.
The microphone output was sampled by an FFT ana-
lyzer and the statistical parameters were calculated. The
spectra of the sound pressure level (SPL) were calculated
for 80 ensemble averages of 2048 data points that were
sampled at 12.8 kHz. The frequency resolution was esti-
mated to be 12.5 Hz.
We measured SPL at attack angle, α, from –30 to 30
degree of Re = 1.5 × 105. The position of porous material
on the airfoil is shown in Figure 3. When the porous
material mounts on the surface of suction side of test
airfoil, α is positive value. Therefore, when α is negative
value, the porous material is located on the surface of
pressure side of airfoil.
2.2. Measurement of Air Permeability
The air permeability rate is in proportion to the pressure
drop, time, and area of porous material, and is in inverse
proportion to the thickness of porous material. Therefore,
the air permeability was defined by
Q
PA

  (1)
where Q is the volume flow rate, δ is the thickness of
porous material, ΔP is the pressure drop, A is the area of
porous material. The experimental apparatus of air per-
meability measurement was shown in Figure 4. μ were
calculated from these values measured by the sensors of
test apparatus in Figure 4. The measured air permeability,
μ, for test porous materials are shown in Figure 5. μ of
Styrofoam (Material A) as porous material became about
10 times larger than that of porous plate (Plate). And μ of
porous plate (Plate) was similar with the results of Poly-
ethylene foam (Material B) at the low flow rate, Q.
2.3. Measurement of Sound Absorbing
Coefficient
The experimental apparatus of acoustic impedance mea-
surement was shown in Figure 6. A test porous material
was enclosed within the test apparatus into which an
acoustic wave was emitted from the loudspeaker. The
+α
Flow
Figure 3. Attack angle and position of porous material.
Packing Fl an ge
Porous material
Flow meter
Va l v e
Pressure sensor
Honeycomb
Air Co mpre ss or
Figure 4. Schematic of test apparatus of air permeability.
0
0.5
1
1.5
02468
μm/(Pa・s)
Qm3/s
10
Pl ate
Material A
Material B
×10
-4
×10
-6
Figure 5. Air permeability against volume flow rate.
Block（hard wall）
Microphone
94×94
Speaker
Packing Flange
710
30 55
510 200
Porous material
Figure 6. Schematic of acoustic impedance tube.
transfer function was measured according to ISO10534-2.
The normal incidence absorption coefficient and acoustic
characteristics were calculated from the obtained transfer
function by using two microphone methods. Its measure-
ing range is 100 - 1500 Hz for a large tube of an internal
cross section of 94 × 94 mm, and 1500 - 5000 Hz for a
small tube of 24 × 24 mm.
Figure 7 shows the absorption coefficients, β, for test
porous materials. The gray dotted line represents the re-
sult for the porous plate. β became high value of 1.0 be-
tween about 3000 Hz to 4000 Hz. The dark solid line and
dotted line are results of Polyethylene foam and Styro-
foam respectively. β of Styrofoam agreed well with that
of Polyethylene foam. β of these materials became about
1.0 about 4800 Hz. As frequency, f, decreased, β of these
materials decreased.

H. HAMAKAWA ET AL. 58
3. Results and Discussion
e Radiated from
rom
normporous material to clarify the ef-
e peak frequen-
ci
3.1. Discrete Frequency Nois
Normal Airfoil
First, we measured the aerodynamic sound radiated f
al airfoil without
fect of porous material on its sound. The gray solid line
in Figure 8 shows a typical spectrum of sound pressure
level (SPL) at attack angle, α, of 0 degree. Multiple
peaks observed in the spectrum of SPL.
Figure 9 shows variation of these peak frequencies of
SPL against freestream velocity, U∞. Th
es were dependent on the freestream velocity 1. 5
U

. For
small variations in the freestream velocity, the frequencies
0
0.2
0.4
0.6
0.8
1
6001600 2600 3600 4600
β
fHz
Material A
Material B
Plate
Figure 7. Sound absorbing coefficient.
10
30
50
70
6001600 2600 3600 4600
SPL dB
fHz
Norma l
Both Sides
R
e
=1.5×10
5
, α=0°
Figure 8. Spectra of SPL of test blades.
0
1000
2000
3000
4000
5000
0 10203040
fHz
U
∞
m/s
∝U
∞1.5
∝U
∞0.8
of these sounds were approximately proportional to 0.8
U

.
At intermittently spaced freestream velocities the -
quency of the sound was observed to jump to other cur-
ves proportional to 1. 5
U
fre

. These are same tendency for
Paterson et al. [4].
3.2. Effect of Local Porous Material on
The erodynamic sound radiated
Aerodynamic Sound
spectra of SPL of the a
from the test airfoils at α = –2 degree were measured.
The porous materials are mounted at the surface of the
pressure side of the test airfoils. The dotted line in Fig-
ure 10 shows the baseline spectrum of SPL for normal
airfoil. Multiple peaks observed in the spectrum as well
as the results of α = 0 degree. The red line and blue line
in Figure 10 show the spectra of SPL for Material B and
Plate respectively. No peaks were formed in these spectra.
The maximum peak level is approximately 51.7 dB lower
than the normal airfoil at 1237.3 Hz. It is clear that these
materials are effective to reduce the discrete frequency
noise radiated from airfoil. However, SPL over 2600 Hz
for Plate increased rather than that for Material B. In
Figure 10, the green dotted line, purple line and yellow
line represent the spectra of SPLs for Material A, Trip
2.6 and Trip 0.8 respectively. The maximum peak level
of Material A is approximately 32.4 dB lower than the
normal airfoil although the multiple peaks observed in
the spectrum. The tripping wire changes the roughness of
the surface of airfoil, and increases the velocity distur-
bance in the boundary layer. This means that the reduc-
tion of peak SPL depends on the intensity of velocity
disturbance in the boundary layer on the surface of the
pressure side of airfoil. On the other hand, the SPLs are
almost same from 2600 Hz to 4600 Hz for all test airfoils.
It is considered that the peak SPL does not depend on the
sound absorption coefficients. The reason for this is that
the area of the porous material is small on the surface of
airfoil.
Figure 11 shows the spectra of SPL at α = +2 degree.
The porous materials are mounted at the surface of the
0
30
60
90
6001600 2600 3600 4600
SPL dB
fHz
Plate
Material A
Material B
Trip 0.8
Trip 2.6
Normal
α=－2°
Figure 10. Comparison of spectra of SPL at α = –2 degree.
Figure 9. Variation of peak frequencies against freestrem
velocity. a

H. HAMAKAWA ET AL. 59
0
30
60
90
6001600 2600 3600 4600
SPL dB
fHz
Plate
Material A
Material B
Trip 0.8
Trip 2.6
Normal
α=+2°
Figure 11. Comparison of spectra of SPL at α = +2 degre
suction side of the test airfoils. The discrete frequency
noise was generated for all test airfoils. In specially, SPL
over 2600 Hz for Plate and Trip 2.6 increased rather than
that for normal airfoil.
As absolute value of α increased, the discrete fre-
quency noise was not generated for normal airfoil. Fig-
ure 12 represents the typical spectra of SPL at α = –6
degree for all test airfoils. The discrete frequency noise
was not generated. The spectra of SPL were almost same
for all test airfoils. It is clear that the porous materials are
not effective to reduce the broad-band noise radied
4.
diated from airfoil was experimentally investigated. As a
e.
at
f
n
rom airfoil at larger α. This indicates that the SPL does
ot also depend on the sound absorption coefficients in
this flow condition.
Figure 13 is the results of α = +6 degree. The discrete
frequency noise was generated for Plate although its
noise was not for the others. The peak SPL of discrete
frequency noise for Plate increased from α = +1 to 9 de-
gree. The Plate was not effective to reduce the discrete
frequency noise radiated from airfoil at larger α. It is
considered that this is caused by the suitable velocity
disturbance in the boundary layer generated from the
porous plate near the leading edge. As absolute value of
α increased more, the discrete frequency noise was not
generated for all test airfoils.
From above discussion, it is considered that Material B
is the most effective to reduce the discrete frequency
noise. Thus, we measured the peak SPL in the case of
Both Sides at freestream velocity from 5 m/s to 45 m/s.
The Material B was mounted on the both surface of test
airfoil as shown in Figure 2(d). The dark solid line in
Figure 8 is the typical result of spectrum of SPL. No
peaks were formed in the spectrum. The gray squares in
Figure 14 are SPL of Both Sides at the peak frequencies
for normal airfoil at α = 0 degree. The peak SPL de-
creased for all velocity range. The maximum drop of
SPL was about 30.7 dB.
Conclusions
The effect of porous material on aerodynamic sound ra-
5
15
25
35
600 1600
SPL dB
2600 3600 4600
fHz
Plate
Material A
Material B
Trip 0.8
Trip 2.6
Normal
α=－6°
Figure 12. Comparison of spectra of SPL at α = –6 degree.
0
20
40
60
80
6001600 2600 36004600
SPL dB
fHz
Plate
Material A
Material B
Trip 0.8
Trip 2.6
Normal
α=+6°
Figure 13. Comparison of spectra of SPL at α = +6 degree.
20
30
40
50
60
70
525
SPL dB
U
∞
m/s
45
Normal
Both Sides
F
result, the following conclusions were obtained:
1) The Polyethylene foam and the Porous plate are ef-
fective to reduce the discrete frequency noise radiated
from airfoil at small attack angle. These materials are
mounted at the surface of the pressure side near the lead-
ing edge of the airfoil. The SPLs of these materials at
1237.3 Hz are approximately 51.7 dB lower than that of
normal airfoil at attack angle of –2 degree. However,
SPL of Porous plate increased rather than that of Poly
ethylene foam over 2600 Hz.
2) As absolute value of attack angle increased, the is-
. The porous materials were not effective to reduce
e broad-band noise radiated from airfoil at larger attack
igure 14. Variation of peak SPL against freestream veloc-
ty. i
d
crete frequency noise was not generated for all test air-
oilsf
th

H. HAMAKAWA ET AL. 60
on c
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the results of Polyethylene foam at low flow rate. Air
permeability of Styrofoam became about 10 times larger
than those of Porous plate and Polyethylene foam.
4) Absorption coefficient of Styrofoam agreed well
with that of Polyethylene foam. These coefficients for
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about 4800 Hz. And as frequen
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5. Acknowledgements
This investigation was supported by a Grant-in-Aid for
Scientific Research through grant number 23560265 from
Japanese Society for the Promotion of Science.
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: Area of porous material (m2)
: Diameter of tripping wire (mm)
0: Hole diameter of porous plate (mm)
Frequency (Hz)
Chord length of airfoil (m
Pa)
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U∞: Freestream velocity (m/s)
α: Attack angle (degree)
β: Absorption coefficient
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Nomenclature Re: Reynolds nu
A
d
d
f:
ℓ:)
ΔP: Pressure drop (
Q: Volume flow rat