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

Predicting cooling fan noise by numerical conditions using
compressible Large Eddy Simulation
Kimihisa KANEKO1; Tsutomu YAMAMOTO2
1,2Fuji Electric Co., Ltd., Japan

ABSTRACTThis paper describes predicting motor fan noise using direct computational aeroacoustics (direct CAA)
methods. In the direct CAA method, both turbulent flow and acoustic phenomenon are solved at the sametime with compressible Navier-Stokes equation. Large Eddy Simulation is applied for solving turbulent flow.
Direct CAA can predict aeroacoustics without any assumption model such as a rotating fan. Therefore highaccuracy results can be obtained. On the other hand, much computational time are required. For the reason,
it is required to reduce the computational time for developing new product with short time period.
We investigated the relation between the computational time and their accuracy. Specifically,computational time step can be reduced computational time, and accuracy were investigated in terms ofpressure fluctuation on the sound source side and acoustic effect on the sound receiver side in this study.
Keywords: Aeroacoustics, Large Eddy Simulation, Compressible turbulence flow

1. INTRODUCTION
Recent trends of electric equipment miniaturization have caused an increase in the heat generation
density and an accompanying need to increase airflow to enable cooling. Therefore, aerodynamic
noise from fans has become a dominant source of noise in air-cooled electrical equipment. Fan noise
is known to be influenced by the fan operating point and the fan's surrounding structures (1, 2, 3).
Predicting the noise level when designing electronic equipment incorporating a fan is important, as isunderstanding aerodynamic noise phenomena under various practical conditions. Nevertheless, it isdifficult to characterize the sound source without considering the structure of the electric components
and the fan. The authors' previous study specifically addressed fan noise using a non-axisymmetricstructure to elucidate the noise-generation mechanism related to the electronic equipment(4).Either
the hybrid computational aeroacoustics (CAA) method or the direct CAA method can be used toconduct a numerical analysis of aerodynamic noise.
The hybrid CAA method uses incompressible Navier-Stokes equations to compute turbulent flow
and the acoustic wave separately. Furthermore, turbulent fluctuation, which is the source of acousticpropagation, is obtainable using several turbulent models: LES, Detached Eddy Simulation (DES),
Unsteady Reynolds Averaged Navier-Stokes (U-RANS), and acoustic propagation are obtainable
using Lighthill's acoustic analogy(5). The effectiveness of using the hybrid CAA method for analyzing
aerodynamic noise from a centrifugal fan(6, 7, 8) and an axial flow fan(9, 10) have been described inearlier reports. Furthermore, predicting aeroacoustics noise of complex geometry such as electronic
devices have been investigated with several U-RANS based turbulent model and acoustics(11).
The direct CAA method uses compressible Navier-Stokes equations to compute both the turbulent
flow and the acoustic wave. High-order numerical schemes must be used to resolve turbulent andacoustic fluctuations(12). Interaction between fluid and acoustics have been investigated using highorder numerical schemes with two-dimensional cavity flow(13, 14).
The authors' previous study addressed axial fan noise prediction with an obstacle effect using direct
CAA method(15). In terms of sound pressure level, our direct CAA model using second order1

kaneko-kimihisa@fujielectric.com

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numerical schemes have been obtained good agreement with the experimental result. As describedherein, we investigated the possibility of the direct CAA method to develop low noise products.
Especially, the sound pressure level (SPL) and pressure fluctuation with the direct CAA model wereverified with experiments for a simplified motor structure.
The authors’ previous study using direct CAA method for predicting motor fan noise, thesimulation model have been obtained good agreement with the experimental result(18). Specifically,
the sound pressure level (SPL) at the observation location and pressure fluctuation in the sound source
field. For conducting the practical application using direct CAA, compu tational time should bereduced. In this study, we investigate the predicting SPL accuracy and their computational timedepending on the time step.

2. EXPERIMENTAL METHOD
2.1 Experimental structure for verification of direct CAA modelFigure 1 portrays the experimental structure for functional verification. This structure comprises
five parts, which is a frame, cooling fin, fan, a fan driving motor, and a cover, to verify aeroacoustics
phenomena. Cooling fins are arranged radially on the frame surface. The fan, which is driven by thefan driving motor, is set at the end of the frame. The fan can be used bi-directionally.
The cover is arranged for flow path and safety purpose. Air flows from outside of the cover throughthe air intake. Air pushed up by the rotating fan flows past the cooling fins. Experimental conditions
are presented in Table 1. The fan rotated between 1000 rpm and 2000 rpm. The typical rotating fan
speed of 1780 rpm is defined for comparison in this study.

(b)Enlargement view(a)Validation structure
Figure 1 – This is a caption for the figure
Table 1 – Experimental setup

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Parameter

Value

Fan diameter D, mm

0.384

Fan blade number Z

17

Rotational speed N, rpm

1780

Blade tip speed uA, m/s

35.7

Re (=uAD/ν)9105

Ma (=uA/c0)

0.1

2.2 Measurement of the pressure fluctuation and sound pressure level
Sound pressure level measurements and hydraulic pressure fluctuation measurements of the soundsource side were taken to verify the numerical simulation results. Pressure fluctuation, which acts on
the solid surface, is measured downstream of the fan. The pressure sensor was placed at the fan cover
via the pressure hole (1mm) with a recessed mounting to obtain the exact measurement position, as
shown in Figure 1(b). However, using this method, the well-known Helmholtz resonance effect occurs.
Therefore, to avoid the Helmholtz resonance in the observation frequency range, the gap dimension
was defined. For analysis of the pressure fluctuation in the frequency domain, the pressure signals
were measured for 500 s. Subsequently, the Hanning window and overlap factor 0.5 for each segment
were used to obtain the power spectra densities. The SPL was measured using a microphone placed at
the rotational fan axis height and 1 m distant from the fan cover in the semi -anechoic room. Theobservation frequency range was as high as 2500 Hz. However, the frequency was as high as 5000 Hz
to elucidate the PSD and SPL trend.

3. NUMERICAL SIMULATION METHOD
3.1 Governing Equation
For predicting aeroacoustic noise, the compressible Navier-Stokes equation and energy equation
are considered. The LES turbulence model is used to solve the turbulent flow. Moreover, the Dynamic
Smagorinsky Model is used as a sub-grid scale model. A Finite Volume Method (FVM) was used tosolve the Navier-Stokes equations with the commercial CFD code star-ccm+.
For spatial discretization of the convective term, Bounded Central Differencing (BCD) scheme
used for obtaining a stable solution for LES. BCD is based on the Normalized Variable Diagram(NVD) approach. BCD can provide good accuracy and robustness compared with the second-order
upwind scheme(16). For temporal discretization, second order implicit Euler method was used.

(a)Isometric view(b)Side view
Figure 2 – Computational domain

3.2 Computational gridComputational grid size defined depending on the dominant physical phenomena, turbulent flow,
or sound wave. Fine grid is required to solve the turbulent flow compare to the sound wave
propagation. A defined computational grid is shown in Figure 3. The grid size controlled divided into
three domains, which is indicated in Figure 2(b). Domain-A: sound wave propagation is dominant.
The sound propagates from the motor fan cover to the microphone, which was located 1m distance.
The grid size was defined based on the point per wave (PPW). Domain-B: turbulent flow is dominant.
The fine grid was made in this area for solving turbulent eddy by LES. The grid size was defined
based on the observation frequency range and Reynolds number. Domain-C: the other area of domain
A and B. The influence of the observation point assumes small. We made a coarse grid to stablenumerical computation.

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(b) Enlarged view around rotating fan(a)Side view

Figure 3 – Computational grid
3.3 Time stepFor evaluating numerical time step dependency on the accuracy of SPL prediction dimensionlessvalue was defined as follows equations. Courant number (CFL), acoustics wave courant number(WCFL) and PPW were used.
‫ݑ‬஺ǡ஻ ή ݀‫ݐ‬(1)‫ ܮܨܥ‬ൌο‫ݔ‬ܿ଴ ή ݀‫ݐ‬(2)ܹ‫ ܮܨܥ‬ൌο‫ݔ‬ܿ଴ܹܲܲ ൌ(3)݂ ή ο‫ݔ‬
Therein, ‫ݑ‬୅ǡ୆ represent typical velocity and subscript indicates domain name. ܿ଴  is acousticvelocity, ݀‫ ݐ‬is time step, ο‫ ݔ‬is grid size, ݂ is maximum frequency range for observation, in thisstudy f = 2500 Hz.
Our defined time step related to the CFL, WCFL and PPW are shown in Table 2. For obtaining thehigh accuracy result, courant number should be controlled under 1.0 in generally, and PPW is above
10.0 (18). CFL and PPW is sufficient value for all time step and domains. However, in the previous
study result, which was defined time step dt = 10 μs, the predicted SPL spectra was in good agreementwith experiment. For reducing computational time, time step dependency was evaluate d as the basecondition is 10 μs.
Table 2 – Defined CFL, WCFL and PPWDomain

AParameter

Time step [μs]101525

CFL[-]

0.010

0.014

0.026

WCFL[-]

0.34

0.51

0.85

PPW[-]
B

CFL[-]

0.35

0.5

0.9

WCFL[-]

3.4

5.1

8.5

PPW[-]

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4. RESULTS AND DISCUSSION
4.1 Turbulent flow
The velocity and averaged pressure distribution are shown in Figure 4. The peak velocity appears
downstream of the rotating fan. The flow is circulated counterclockwise by the fan rotation; after it
bends 90 deg, it flows between the each cooling fins. Averaged pressure fluctuation indicated as root
mean square is shown in Figure 5. High-pressure fluctuation occurs between the leading edge of theblade and downstream of it. Especially, pressure fluctuation increased at the leading edge of the blade,and fan base plate between the blades. The leading edge of the blade, which is close to the intake, isinfluenced at least eight times by the intake fluctuation per rotation. The fan base plate, which isbetween the blades, influences the separation flow of the suction side blade.
For analysis of the turbulent flow, the instantaneous second invariant of the velocity gradient tensor,
called the Q-criterion, is shown in Figure 6. The Q-criterion indicates and iso-surface colored withvelocity magnitude. The Q-criterion is distributed around the rotating fan and downstream of it. A
large-scale voritical structure is apparent at the leading edge side of the blade because secondary flowoccurs by the separation and leakage flow of the blade. A small-scale voritical structure is distributednear the curved motor frame surface caused by separation flow with a swirl flow.

Figure 4 – Velocity distribution (Instantaneous)Figure 5 – Pressure distribution (RMS)3159

Figure 6 – Q-Criterion distribution colored with velocity (ܳ ൌ ͳǤͷ ൈ ͳͲ଻Τ‫ ݏ‬ଶ)
4.2 Pressure fluctuation in the sound source
For verification of the pressure fluctuation, the computed result and the measured result arecompared with power spectra density (PSD), which are shown in Figure 7. Predicted pressure
fluctuation PSD results are in good agreement with the measured results up to 2500 Hz of ourobservation range. A computed PSD trend above the 2500 Hz range is slightly decreasing because thecomputational grid resolution of LES is insufficient. Pressure fluctuation consists of the dominantfrequency and broadband frequency. The dominant frequency is blade passing frequency (BPF), which
is based on the blade number and fan rotating frequency. Predicted pressure fluctuation can be solvedBPF. The broadband frequency is the influence of turbulent flow. Pressure fluctuation decays above
approximately 500 Hz. The trend of their decay is proportional to the frequency of multiplied by -7/3.
Pressure fluctuation in the inertial subrange of turbulent flow shown as the following equation(17).
(4)‫݌‬ሺ݇ሻ ൌ ݇ ି଻ΤଷIn that equation, ݇ expresses a wave number, which is related to the unsteady turbulent flow
frequency. As for various time step, the trend of pressure fluctuation PSD and their value are obtained
close to measurement result. However, it was found increasing the time step, decreasing the PSD athigh frequency range.

Figure 7 – Pressure fluctuation PSD at each time step3160

4.3 Sound pressure level
The SPL spectra at the observation point are shown in Figure 8. The SPL includes BPF, broadband
noise which cased turbulent flow, and acoustic mode which caused geometry. Predicted SPL with dt= 10 ߤ‫ ݏ‬was in good agreement with the experimental result. The trend decay of SPL was influenced
by the computational time step. As the time step increases, the SPL decay increases. Decayed the SPLspectra much lower frequency compare to the pressure fluctuation. As the frequency is higher, thepropagated pressure wave number per time step is increased. Therefore, a high-frequency pressure
wave is influenced numerical dissipation compare to the low-frequency. For verification of the SPL
decay, sinusoidal frequency pressure source ‫݌‬௕௖ , which shows the following equation, defined insideof the fan cover, which assumed sound noise by the rotating fan.
‫݌‬௕௖ ሺ‫ݐ‬ሻ ൌ ‫݌‬௔௠௣ ሺʹߨ݂‫ݐ‬ሻ (5)Therein, t is time, ‫݌‬௔௠௣ is the amplitude of source pressure, f (= 500 Hz, 2500 Hz) is frequency.
Dimensionless pressure,‫݌‬Ȁ‫݌‬௔௠௣ , shows in Figure 9. It was confirmed that the propagated pressure
decays at high-frequency was affected by the time step compared to the low-frequency with simplified
pressure source conditions.

Figure 8– SPL at observation point at each time step

Figure 9 – Dimensionless pressure distribution at each time step and frequency (Instantaneous)3161

5. CONCLUSIONSThe Direct CAA method applies to predict aeroacoustics noise to develop low noise products. Thismethod can predict sound propagation and turbulent flow simultaneously. On the other hand, direct
CAA method is required much computational time compared to the hybrid CAA method, since small
time step is needed.
For developing stage of products by using direct CAA method, short computational time andaccuracy are required. Therefore, we investigated the time step dependency for accuracy. From ourresults, we conclude as follows.
(1) Predicted pressure fluctuation PSD and SPL spectra are in good agreement with theexperimental result.
(2) Predicted the PSD is in good agreement, not only the BPF but also the trend of PSD decay inthe turbulent inertial region corresponds to the experiment.
(3) The computational time step for predicting SPL is more influenced compare to predicting PSD.

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