PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Prediction Methodology of Broadband Noise from a Cooling FanSoichi SASAKI 1
1Nagasaki University, JapanABSTRACT
The experimental prediction methodology of the fan noise as the first step to organize the blade
elementary angular momentum theory is proposed. For the prediction equation of the broadband noise,
the theory on the acoustic radiation from airfoil with turbulent boundary layer is applied. The
broadband noise of the cooling fan is predicted experimentally by using the measured flow regime inthe wake of the actual fan based on the results of wind tunnel test on the aerodynamic noise of a flatplate. The prediction by the suggested methodology could explain the reduction of the broadband
noise in the low frequency domain in the operation point of the cooling fan is the effect of thereduction of the wake vortex noise made by the pressure side separation.
Keywords: Broadband Noise, Blade Element, Wind Tunnel, Low Pressure Fan

1. INTRODUCTION
Propeller fans are used as a cooling fan for the heat exchangers in HVAC systems (heating,ventilation, air conditioning, systems). For example, in recent years, the R & D of the small output
Organic Rankine Cycles using a low-grade heat source such as hot spring water has been promoted(1) . In this cycle, the low boiling point refrigerant such as R245fa is used as the working fluid; thecooling fan is used for condensing the working fluid. Because the cooling fan in the HVAC system
cools the heating device by its own velocity, it has no duct and is almost no increase the static press ureof the fan. Under such conditions, in the case of the low solidity impeller, the flow passing throughthe blade can be handled as two-dimensionally.
The blade element momentum theory (BEM) is the theory which is handled the flow passing
through the blade element in two dimensions (2) . The theory has been practical used to calculate thelocal forces on the blade on the wind turbine (3). Even in the case of the wind turbine, the staticpressure rise of the flow passing through the impeller is small. It makes possible to handle the flow
around the blade elements as a simplified two-dimensional flow. Author predicted the broadband noise
generated from a horizontal axis wind turbine based on BEM by applying the characteristics of thetwo dimensional flow (4). An analytical model proposed by M. Roger and S. Moreau was used for thebase principal to predict the broadband noise (5) . However, there are some difficulties in the handlingof the radiation integral and statistical pressure fluctuation model in the practical using for the des ignof the fan. T. Fukano et al., proposed the prediction theory on the aerodynamic noise generated froman axial fan with the wake characteristics of the impeller (6) ; however, the theory cannot express thespectral distribution of the broadband noise because the overall noise level is predicted.
By the way, the cooling fan in the HVAC system is also small static pressure rise, so it makes
possible to replace the flow in the blade elements as the two -dimensional flow. In the case of thedesign for the impeller of the fan, the theoretical total pressure based on velocity triangle and theirangular momentum is used as the basic principal. If the principal of the velocity triangle and angularmomentum is applied to fan noise prediction, it is possible to predict fan noise by the blade ele ment
theory. Therefore, in this study, the methodology to predict the fan noise experimentally based on themeasurement of the wake as the first step to organize the blade elementary angular momentum theory
is proposed. For the prediction equation of the broadband noise, the theory suggested by B. D.
Mugridge which is acoustic radiation from airfoil with turbulent boundary layer is applied (7). In the11820

souichi@nagasaki-u.ac.jp

suggested methodology, the broadband noise of the cooling fan is predicted experimentally by using
the measured flow regime in the wake of the actual fan based on the results of wind tunnel test on theaerodynamic noise of a flat plate.

2. EXPERIMENTAL SETUP
2.1 Experimental Apparatus
The wind tunnel for the measurement of the properties of the flap plate is shown in Fig.1. The sizeof the square nozzle is 100mm. When the Reynolds number is approximately 2.0 × 10 5, the turbulenceof the main flow within the measurement region is less than 0.5%. The leading edge of the blade isset at 100 mm downstream from the nozzle exit. A 1/2-inch microphone (Ono-Sokki, LA-4350) is set
at a distance of 0.5 m from the trailing edge; the angle between the main flow and the microphone is90°. The signal from the noise level meter is sent to the FFT analyzer (Ono -Sokki, CF5210), and thefrequency response characteristics of the noise are analyzed. In this measurement method, we discuss
the far field noise properties than the wave length of the point sound source without take into accountof the directivity. The blade chord is 40mm, the span length is 100mm, the thickness is the 2mm. The
angle of attack is defined as the angle formed by the center line of the blade and the stream line of themain flow.

Nozzle䠄䕕100mm)

Plenum
Box

0.5 m
0.1 m

FFT
Analyzer

Noise Level
Meter

Fig. 1 Experimental setup of the wind tunnel test for the flat plateIn Fig. 2, the schematic diagram of the test bench for the estimation of the fan performance isshown. The diameter of the impeller is 613 mm, the hub ratio is 0.424 and number of blades is 14.
The height and width of the duct are 1 m each, while its total length is approximately 4 m. The dynamic
pressure is measured 600 mm upstream of the impeller disc using a Pitot tube. From the results of thevelocity distribution for the estimation of the flow rate, the flow coefficient was found to be 0.842.
The flow rate is deduced from the dynamic pressure. It is controlled by an adjustable throttle at theduct exit. The static pressure of the fan is measured 400 mm upstream of the exit. The rotational speedof the driving shaft is 1200 rpm. I measured the shaft torque of the motor using a torque meter (OnoSokki; SS-500), and the efficiency of the fan was estimated based on the ratio of shaft power totheoretical power. The normalized characteristics of the fan are summarized as follows;

M4Q,\ sȧ(1 Ȥ2 ) D2 U

2Ps,OU U28L,K
U S (1 Ȥ2 ) D2 U 3I\sO(1)

where the φ is the flow coefficient, ψs is the static pressure coefficient, λ is the power coefficient, andη is the efficiency. A 1/2-inch microphone (Ono-Sokki, LA-4350) is set at distance of 1.0 m from theimpeller inlet on the rotational axis of the impeller. The frequency response of the measured fan noiseis provided by a Fast Fourier Transfer analyzer (Ono Sokki, CF5210).

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DZ

613 mm14

ν
4.0 m
 

1.0 m

1.0m



1.0m


0.424






StrutTorque Motor
Meter



Noise
LevelMeter

TorqueStrut Meter

Motor

Impeller

ImpellerDamperDamper(a) measurement for the aerodynamic characteristics(b) measurement method for the noise

Fig. 2 Schematic diagram of the test bench for the estimation of the fan performance
In Fig. 3, the measurement method of the flow regime in the wake of the impeller is shown. The
wake of the impeller is measured by an X type hot-wire probe (KANOMAX, 0249R-T5). The X type
hot wire probe can measure the simultaneously the two velocity components. The hot -wire probe isattached to the traverse machine; the arbitrary flow field is measured by controlling the stepping motor.
The flow regime near the blade tip is measured 160 mm in the mainstream directions and 240 mm in
the radial directions. The measurement position of the wake is 5mm behind the trailing edge of theblade.
160240㻿㼡㼏㼠㼕㼛㼚㻌㻿㼡㼞㼒㼍㼏㼑x㻼㼞㼑㼟㼟㼡㼞㼑㻌㻿㼡㼞㼒㼍㼏㼑yMain flowvθ

Traversemachiner = 230mmv
αvzβθw+δuFig. 3 Measurement method of the flow regime

Fig. 4 Velocity triangle in the wake

2.2 Prediction Methodology of Broadband NoiseIn Fig. 4, the velocity triangle in the wake of the impeller is explained. The X type hot-wire probe
can measure the axial velocity component vz of the absolute velocity and the circumferential velocity
component v θ. Then, the absolute velocity and the absolute outflow angle are given by equation ( 2).

vvx 2  vT 2 , Dtan 1vxvT(2)At this time, the relative velocity w and the relative outflow angle β become Equation (3).

wu  v  2 u v cosȘ , E22§ u 2  v 2  w2 ·cos ¨
¸2uw
©
¹
1(3)

When the setting angle θ of the impeller is known, the outlet deviation angle δ is expressed as follows;G E T(4)where, the angle of the pressure side is defined as positive. According to reference (7), the soundpower radiation by a number of flat plate or airfoils, each having a surface pressure distribution causedby the turbulent boundary layers, may be written as;

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dEdZ

N L w3ȭpp (Z ) , 1 ! S c / O ! 0.4M ; b  O ; M ! 1/14
6 S Z U a0(5)where, E is the sound power, N is the number of blades, L is the span of the blade element, w is therelative velocity, φ pp is the wall pressure spectrum density. The statistical wall pressure spectrum
density suggested by B. D. Mugridge is given as;

ȭpp103 U 2 G w3 , G

0.093
0.09 c Re 0.2(6)where, δ is the boundary layer displacement thickness. The boundary layer displacement thickness isevaluated by the exponential law. The ratio on the sound pressure p 2 of the measured value of themodel in the wind tunnel test to the target value of the blade element in the actual fan is given by;

po 2pm 232

N o Lo § wo · § Zm ·§ rm · ȭpp (Z )o,¨¸ ¨¸¨ ¸N m Lm © wm ¹ © Zo ¹© ro ¹ ȭpp (Z )mE2

4 S r2p23 U a0 cos 2 T(7)where, subscript m is the model value, o is the objective value of the blade element for the target fan.
In the case of the noise level, since decibel notation is common, let me express equation ( 8) aslogarithm.
§N ·
§L ·
§w ·
Lp o Lp m  10 log ¨ o ¸  10 log ¨ o ¸  30 log ¨ o ¸© Nm ¹© Lm ¹© wm ¹(8)§ ȭpp (Z )o ·§ Zm ·§ rm ·
 10 log ¨¸¸¸  20 log ¨ ¸  10 log ¨¨© Zo ¹© ro ¹©ȭpp (Z ) m ¹
In the experimental analysis of the broadband noise using this methodology, the target noise level ofthe fan can be predicted by the model size and test condition in the wind tunnel test and the scale anddriving condition of the actual fan.

3. RESURLT AND DISCUSSIONIn Fig. 5, the aerodynamic characteristics of the fan is shown. The highest efficiency point of thisfan is φ = 0.3. The operating point of the cooling fan is set to φ = 0.43, which is close to theatmospheric pressure. The characteristics of the sound pressure level of the fan is presented in Fig. 6.
The fan noise at the operating point of the cooling fan was 0.8 dB greater than that at the highest
efficiency point.
110

0.51000.6

ψ

η

0.4

0.2
λ0.2

0.1
0.2

0.3

0.4

ȭ
Fig. 5 Aerodynamic characteristics

00.5

89.6 dB

88.8 dB90
N = 1200rpm
Z = 1480ȭ = 0.43

ȭ = 0.3

ȭ=0.43

ȭ=0.3

00.1

Lp , dBȯ,Ȟ

0.30.8ȢN = 1200 rpm
Z = 140.4

ȭ
ȯ
Ȣ

70
0.1

0.2

0.3

0.40.5

ȭFig. 6 Noise characteristics

The spectral distribution of the fan noise at the highest efficiency point and the working point iscompared in Fig.7. The fan noise at the operating point was increased by 0.8 dB; however, it is theinfluence on the discrete frequency noise synchronized with the blade passing frequency; whereas,
we can notice the sound pressure level of the operation point in the domain lower than 200 Hz became
clearly low than that of the maximum efficiency point. In Fig.8, the distribution of absolute velocity
in wake measured by the hot-wire anemometer is shown. The absolute velocity is distributed in the1823

axial direction of the impeller. This result indicates that the direction of the momentum of the wakeflow is directed in the axial direction; in particular, the velocity distribution gives the information thatthe two-dimensional flow field is formed in the area of a mid-span.
䢴䢲䢲

䢳䢶䢲

N = 1200 rpm
Z = 14
ȭ=0.3Blade Tip

䢳䢲

䢳䢷

䢴䢷

䢳䢲䢲

䢵䢲

䢳䢷
䢴䢲
䢸䢲
䢴䢷

Background noise (66.1 dB)

䢵䢷䢴䢲

䢵䢷

䢵䢷
䢵䢷

䢵䢲

䢴䢷

䢺䢲

䢸䢲

䢳䢶䢲

104

䢳䢴䢲

103

䢶䢲

䢲
䢲

102

䢵䢲

䢶䢲

䢴䢲

0䢴䢲䢳䢴䢲

䢺䢲

50

䢳䢷䢴䢲

䢳䢲

䢳䢲䢲

DFN (280Hz)

ȭ=0.3 (88.8 dB)
ȭ=0.43 (89.6 dB)

y , mmLA , dB100

䢳䢲

N = 1200 rpm 䢳䢺䢲Z = 14
䢳䢸䢲
φ = 0.30

x , mmf , HzFig. 7 Spectral distribution of the fan noiseFig. 8 Velocity distribution in the wakeThe flow regime of the impeller in the wake measured by the hot-wire anemometer is presented inFig. 9. The operating point is the maximum efficiency point. In Fig. 9(a), the relative velocity in thevicinity of the blade tip becomes the high velocity. In Fig. 9(b), the distribution of the deviation angle
indicates that the relative flow is separated to the way of the pressure surface side over the wide span
range of the impeller. The deviation angle is the equivalent scale to the angle of attack in the windtunnel test. The angle in the domain of the high relative velocity is about 20 °.

40
N = 1200 rpm
Z = 14
ȭ =0.30

20

ț, deg.

w m/s

60
40
20
00.4

0-20

hub

PS separation

tip

0.6

0.8
r/R
(a) relative velocity

1.0-40N = 1200 rpm
Z = 14
ȭ =0.30

SS separation

tip

hub

0.4

0.60.8r/R
 (b) deviation angle

1.0Fig. 9 Flow regime in the wake of the impeller
In Fig. 10, the characteristics of the sound pressure level of the flat blade is presented. The
horizontal axis is the angle of attack; the vertical axis is the sound pressure level. The negative angle
is the situation that the noise is measured from the suction side, whereas, the positive angle ismeasured from the positive pressure side. The spectral distribution of the sound pressure level of theflat blade is shown in Fig. 11. The angle of attack is 20 °. The thin solid line in the figure is the spectral
distribution of the background noise of the wind tunnel. The thin solid line is the background noise ofthe wind tunnel. In the case of the flat plate with the chord length of 40 mm, the thickness of the shear
layer is approximately 28 mm (D = 40 sin α + 2). At this time, if Karman vortex street is formed in
the wake, the vortex shedding frequency becomes approximately 214 Hz ( f= S t U / D) according to
the Strouhal number relation. The noise of the flat plate increases in the frequency domain of 100 Hz
to 400 Hz.

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8278

Ș=20 deg. ( 78.5 dB )50

Background noise ( 77.1 dB )76

Background noise ( 77.1 dB )PS sideSS side74-40

U = 30.0 m/s
C = 40 mm
4Re = 8.0  10100
Lp , dB

Lp , dB80

U = 30.0 m/s
C = 40 mm
L = 100 mm

0-20

02040
Ș , deg.
Fig. 10 SPL characteristics of the flat plate

102103104
f , HzFig. 11 Spectra of SPL of the flat plate

In Fig. 12, The measured broadband noise of the fan is compared with the predicted one. The
predicted broadband noise level was more than 10 dB higher than the measured value; this result
indicates that the impeller itself becomes an acoustic impedance. The predicted broadband noise could
represent the tendency of the measured value. From the results in Fig. 11, it is recognized that thereduction of the broadband noise in the low frequency domain in the operation point of the cooling
fan is the effect of the reduction of the wake vortex noise made by the pressure side separation.

LA , dB100

ȭ=0.3 (88.8 dB)
ȭ=0.3 (prediction; 99.8 dB)
ȭ=0.43 (89.6 dB)
N = 1200 rpm
Z = 14
ȭ=0.350Background noise (66.1 dB)

0102

103

104

f , HzFig. 12 Comparison on the measured SPL spectra with the prediction

4. SUMMARY
The sound pressure level of the operation point of the cooling fan became decrease than that of themaximum efficiency point in the domain of the low frequency. The relative flow is separ ated to theway of the pressure surface side over the wide span range of the impeller in the maximum efficiency
point. The prediction methodology on broadband noise of the fan could represent the tendency of themeasured value. The prediction by the suggested methodology could explain the reduction of thebroadband noise in the low frequency domain in the operation point of the cooling fan is the effect ofthe reduction of the wake vortex noise made by the pressure side separation.

ACKNOWLEDGEMENTS
This work was supported by JSPS KAKENHI Grant Number 16K00653.

REFERENCES
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2. H. Snel, Review of the Present Status of Rotor Aerodynamics. Wind Energy. 1998; 1: 46-69.
3. Zhenye Sun, Jin Chen, Wen Zhong Shen, Wei Jun Zhu, Improved blade element momentum theory forwind turbine aerodynamic computations. Renewable Energy. 2016; 96: 824 – 831.
4. Soichi Sasaki, Shinsuke Mukae , Ken Tsushima , Experimental Prediction of Performance andBroadband Noise of a Wind Turbine by Blade Element Theory. Proc. ISROMAC2017; 16-24 December
2017; Honolulu, Hawaii 2017. 8 pages.
5. M. Roger and S. Moreau, Back-Scattering Correction and Further Extensions of Amiet’s Trailing Edge
Noise Model. Part I: Theory. Journal of Sound and Vibration. 2005; 286: 477-506.
6. FUKANO, T., TAKAMATSU, Y. and KODAMA, Y., The effects of tip clearance on the noise of low
pressure axial and mixed flow fans. Journal of Sound and Vibration. 1986; 105(2): 291-308.
7. B. D. Mugridge, Acoustic radiation from aerofoils with turbulent boundary layers. Journal of Sound andVibration. 1971; 4(22): 593-614.

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