A06:
FLOW ACOUSTICSABS-0057

Effect of fillets installed in appendages on tonal noise of submarine propeller
Sang-Jae YEO1,2 , Suk-Yoon HONG1,2 , Jee-Hun SONG3
1 Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul, South Korea
2 Institute of Engineering Research, Seoul National University, Seoul, South Korea
3 Department of Naval Architecture and Ocean Engineering, Chonnam National University, Yeosu, South Korea

ABSTRACT
Submarines are equipped with appendages, such as sail and rudders, to perform operations such as maneuver,detection, and communication. The appendages are functionally essential structures but have a negative impact,from the stealth point of view, on the submarine. In this study, the acoustic effect of unfavorable flow, such as
horseshoe vortex (HSV) generated around the appendages, on propeller radiated noise was analyzed. To analyze
this, a frequency-domain noise model is developed, which can predict the noise of an underwater propeller
placed in a non-uniform wake. To clearly analyze the acoustic effects of HSV around appendages, fillets are
installed at the junctions of a submarine where HSV is generated intensively, and the acoustic effects before
and after the installation of the fillets are compared. Through the noise contribution analysis, it was found that
installing fillets on rudder and sail is effective in reducing BPF noise.

Keywords: Submarine, Flow-noise, Horseshoe Vortex

1

INTRODUCTION

In submarines, stealth is the most important performance because it is directly related to survivability. In theunderwater environment, amongst the stealth-related factors, underwater radiated noise (URN) is a key determinant of a submarine’s performance. From the past, as advanced technologies for reducing machinery noise ofsubmarines have been developed and applied, the research interest and importance of technology have continuously shifted towards flow noise. In a submarine, the blade-passing frequency(BPF) noise generated from thepropeller has the highest noise level in non-cavitating operation.
Since BPF noise of the submarine is mainly caused by the unsteady load applied to the propeller, it isgreatly affected by the wake distribution in which the propeller operates. The wake distribution contains detailed
information about the unfavorable flows caused by submarine appendages located upstream of the propeller.
As a prime example, a submarine rudder produces a strong four-cycle wake, but appendages that are farther
away from the propeller or smaller in size also contribute in some way to the wake distribution. Amongthe unfavorable flows from the appendages, the vortex pair called the horseshoe vortex(HSV) generated at thejunction of the appendages and the hull is strong enough to flow into the downstream propeller and cause
various adverse effects.
Recognizing this phenomenon, various studies on the fillet structure, which are known to be effective in
reducing HSV, are being conducted. Devenport et al. (1) found the vortex reduction effect when a fillet of asize similar to the thickness of the appendage was installed on the sail. Zess and Thole (2) found that the HSV
reduction effect of a gas turbine was found when a fillet of a size similar to the thickness of the boundary
layer was installed. After that, Toxopeus et al. (3) performed numerical analysis of the submarine according tovarious dimensions of the fillet mounted on the leading edge of the sail, and revealed that the reduction effectincreases as the size of the fillet increases. Liu et al. (4) revealed that when vertical baffles are installed on
both sides of the sail leading edge, it generates a reverse vortex and breaks down the horseshoe vortex core.
Most of the previous studies have focused on hydrodynamic methods to reduce HSV generated from appendages. However, HSV not only complicates the flow field around the submarine, but also causes a fatal

negative effect of increasing the submarine flow noise. HSVs generated from sail and rudder are strong enoughto flow into the propeller via the hull. The periodic rotation of the submarine’s propeller in the non-uniform
wake generated by the HSV creates additional noise sources of specific frequencies associated with the upstream
appendages. The purpose of this study is to analyze how unfavorable flows such as HSV contribute to the negative effect of increasing propeller BPF noise. In order to clearly analyze the acoustic effect of HSV, fillets
were installed at the junctions of submarine where HSV intensively generated, and compared with that before
installation. In addition, a frequency domain noise model was developed and applied to quantitatively analyze
the occurrence and change of unsteady sources due to the interaction of submarine propeller and appendages.

2

ACOUSTIC MODEL FOR PROPELLER BPF NOISE

2.1 Acoustic analogy
In order to calculate the BPF noise generated by the propeller rotating and moving forward, it is convenient
to introduce a helical coordinate system (5). The r0 , ξ0 , γ0 helical coordinate system is set as the trajectory
sweeping by the pitch change axis of the blade. Now, if the helical coordinate system is applied for the
acoustic analogy, the source can be expressed as a function of convection with velocity U0 in the −γ0 direction.
And, in order to consider the change of the source with time in the blade-fixed frame, the frequency ω0 is
extracted through the Fourier series and expressed as the following formula (6):
δ (t − τ − R/c0 )dγ0 dξ0 dr0 dτ,(1)
4πR
where, g denotes the generalized source function moving along a helical trajectory according to the source time
τ, expressed as:p′ (x,t) =Z ∞ Z ∞Z ∞ Z ∞−∞ 0g(γ0 +Uτ, ξ , r0 ) = ρ0U0−∞ −∞g(γ0 +U0 τ, ξ0 , r0 )e− jω0 τ ×∂Vn (γ0 , r0 )∂ D(γ0 , r0 )
δ (ξ0 + FA) +δ (ξ0 + FA) + L(γ0 , r0 )δ ′ (ξ0 + FA),
∂ γ0
∂ γ0

(2)

here, the first term including Vn corresponds to a thickness noise source, and the second and third terms expressed by D and L correspond to loading noise sources. D and L are the drag and lift forces acting on theblade elements, respectively. FA means the face alignment of the blade element, and indicates the deviation inthe ξ direction from the pitch change axis.
2.2 Frequency-domain unsteady noise model for propeller
Thickness noise is caused by the normal velocity corresponding to the displacement of the surrounding fluidby the movement of the blade element. In previous studies, the approximation formula as in Equation (3) wasapplied to the geometric data of the blade section to estimate the normal velocities.
Vn (γ0 , r0 ) = Vn,top +Vn,bottom≃ U0 (r0 ) (sinθu + sinθl ) ≃ U0 (r0 ) (tanθu + tanθl ) ≃ U0 (r0 )∂ h(γ0 , r0 )
.
∂ γ0

(3)

However, the thickness noise source derived with a constant inflow velocity U0 and a fixed geometry has
no component that fluctuates with time in the blade-fixed frame, so it has a purely steady source characteristic.
When the inflow velocity U0 changes with time, the normal velocity generated on the upper and lower sides
changes, that is, an unsteady component of thickness noise is additionally generated. The unsteady thickness
noise can be expressed by converting the varying inflow velocity U0 (τ) into a Fourier series:
Vn (γ0 , r0 , τ) =U0 (r0 , τ) [sin(θu − θAOA ) + sin(θl + θAOA )] ≃ U0 (r0 , τ) [θu + θl ] cos (θc − θAOA )∞= ∑ Uk (r0 ) [θu (γ0 , r0 ) + θl (γ0 , r0 )] cos (θc (γ0 , r0 ) − θAOA (r0 )) e− jωk τ ,

(4)

−∞

where, Uk represents the periodically fluctuating inflow component with k-order unsteady harmonics. In addition,
the angle of attack (AOA) term, which was ignored, was added to consider the change in the angle of incidence

of the inflow. By substituting the developed unsteady thickness noise formula into Equation (2), the following
thickness noise equation is derived:∞∞− jρ0 c20 B
j (mB−k)(φ −φb0 − π2 )+mB rΩ
c0 −Ωte∑∑8π(r/D)(1 − Mx cosθ ) m=−∞ k=−∞
Z tip mBz0 MT sinθj(φo +φs )×
Mr eJ(mB−k)× [kxUk ΨV (kx )] dz0 ,1 − Mx cosθ
root


h

pthickness =

i

(5)

where, B is the number of propeller blades, m is the order of the BPF noise, r is the distance between receiverand the propeller, θ is the angle between the receiver and the x-axis, φ is the azimuthal angle of receiver,
φb0 is the azimuthal angle at initial position of blade, φo and φs are the phase lag due to offset and sweep,
respectively, J is the Bessel function of the first kind, z0 is the distance between center of propeller and theblade element, Mr = U0 /c0 is the relative Mach number of the blade element, Mx = V0 /c0 is the x-direction
Mach number, and, MT = Ωrt /c0 is the tip rotational Mach number. kx , ky are chordwise wave numbers andthickness-wise wave numbers, respectively, and are defined as follows:




mB
−2 mB(Mr2 cosθ − Mx )2MT
− k BD , ky =+ kMx BD ,(6)
kx =Mr 1 − Mx cosθz0 Mr
1 − Mx cosθZ 1/2

ΨV (kx ) =−1/2[θu + θl ] cos (θc − θAOA ) e jkx X dX,(7)

here, ΨV is the nondimensional source transform of the thickness noise in the frequency-domain. The generalized source function expressed in Equation (2) means the unsteady sources that periodically oscillate with afrequency w0 according to time. In the case of a propeller in non-uniform wake, since unsteady loading components of D and L appear in the harmonics of the angular frequency Ω = 2π times rotational frequency, so it
can be expressed through the following Fourier series:∞

D(γ0 , r0 ,t) = ∑ Dk (γ0 , r0 )e− jωk t ,
k=−∞

(8)

∞

L(γ0 , r0 ,t) = ∑ Lk (γ0 , r0 )e− jωk t ,k=−∞where, ωk = kΩ is the harmonics of the angular frequency. Lk and Dk are the lift and drag components of
k-order unsteady harmonics, respectively. By substituting the unsteady loading source into Equation (2), theloading noise generated from the propeller is expressed as the following formula (7):∞∞− jρ0 c20 B
j (mB−k)(φ −φb0 − π2 )+mB rΩ
c0 −Ωte∑∑8π(r/D)(1 − Mx cosθ ) m=−∞ k=−∞

 

Z tip
mBz0 MT sinθ
CDk
CLk
×
Mr2 e j(φo +φs ) J(mB−k)× kx
ΨDk (kx ) + ky
ΨLk (kx ) dz0 ,1 − Mx cosθ
2
2
root
h

ploading =



i

(9)

where, ΨDk and ΨLk are nondimensional source transforms in the frequency-domain:
Z 1/2

ΨD or L =−1/2

fD or L (X)e jkx X dX

(10)

where, fD and fL represent the distribution factors of drag and lift with unit area and X is the nondimensional
chordwise distance from -0.5 to 0.5.

Figure 1. Geomtries of submarine and propeller (left) DARPA Suboff (right) INSEAN E1619

3

HYDRODYNAMIC EFFECTS OF FILLETS

In this section, before moving on to the hydroacoustic analysis stage, numerical simulation using CFD is performed to extract the unsteady force data input to the noise prediction. In addition, the hydrodynamic effect of
installing fillets at the intersection of hull and appendages is analyzed. The overall structure of the study consists of analysis and experimentation in parallel. The validity of the analysis for submarines is investigated bycomparing the analysis results and experimental measurement results under the same conditions with the target
model. Afterwards, the hydrodynamic and hydroacoutic effects from the installation of the fillets are analyzed
through a verified method. The submarine used in the study is a DARPA Suboff AFF-8 and is equipped withan E1619 propeller developed by INSEAN. Table 1 shows the main particulars of submarine and propeller.
Table 1. Specifications of model
Description

SymbolDimension

DARPA Suboff

Length overallLoa

4.356 mINSEAN E1619

Blade number

B

7

Propeller diameter

Dp

0.262 mThe fillet is known to be effective in suppressing flow separation around the obstacle by resolving thediscontinuous pressure gradient generated at the junction. Fillet was installed in each of the front and rear 10
places of the junction between the appendages and the hull where the vortex is intensively generated. Figure2
and Figure 3 show the results of hydrodynamic analysis of the submarine with and without the fillets. The color
applied to the surface of the submarine indicates the absolute total pressure, which allows the distribution ofpressure along the submarine hull to be investigated. The color that appears on the streamline superimposed on
the surface of the submarine indicates the vorticity at the location, and the more red it appears, the stronger thevortex flow. In the submarine without fillets, the high pressure generated at the leading edge of the appendages
spreads through the intersection to the hull surface, forming a strong adverse pressure gradient. The streamline
flowing toward the appendages along the hull surface is separated due to the adverse pressure gradient to forma strong vortex. The strong vortex generated at the front of appendages goes downstream along both sides of
the appendages to create a HSV composed of a pair of symmetrical flows. In the same way as the leading edge
case, the high pressure formed at the trailing edge of the appendages also generated a adverse pressure gradientat the intersection with the hull, create a root vortex.
On the other hand, when the fillets are installed, the high pressure generated at the leading edge of theappendages and the low pressure of the hull deck are gradually connected along the convex fillet, so that theadverse pressure gradient is relieved. The convex fillet at the front of the appendages reduces the separation of
the streamline and suppresses the HSV. Similar to the front fillet, the concave fillet at rear of the appendages

Figure 2. Pressure distribution around sail and vorticity along streamline (left) submarine without fillets (right)
submarine with fillets

Figure 3. Pressure distribution around rudder and vorticity along streamline (left) submarine without fillets(right) submarine with fillets
smoothly connects the trailing edge and the hull surface, thereby resolving the adverse pressure gradient andsuppressing the root vortex.

4

HYDROACOUSTIC EFFECTS OF FILLETS

The horseshoe vortexes generated from the appendages flow into the propeller along the hull surface. Figure
4 shows the velocity distribution at the propeller plane. In the case of the submarine without fillets, it can beseen that strong vortexes are flow into the propeller. A low axial velocities appear at a locations where thestrong vortexes flow in, because the flow velocity in the core of the vortex is generally reduced compared tothe surrounding flow field. This local decrease in flow velocity forms a circumferential non-uniform velocity
distribution, and the angle of attack(AOA) and inflow velocity change according to the angular position of
the propeller causing unsteady forces. On the other hand, when the fillets are installed, the axial velocity
distribution becomes relatively uniform due to the weakening of the vorticity. An unfavorable flow, such as ahorseshoe vortex, from the submarine appendages interacts with the propeller in a way that induces an unsteadyforce on the blades. When the fillets are installed in front and rear of the appendages, the interaction between
the appendages and the propeller is effectively suppressed by reducing the generation of vortex.
Figure 5 is a schematic diagram showing the extraction of unsteady noise sources. During one revolution
within the non-uniform wake, the force applied to the reference blade marked in red changes according to the
angular position of the blade. Among them, the 4th harmonic source like the blue line is mainly generated fromthe 4-cycle wake from the rudder, and the 8th harmonic source shown in green line is mainly caused by the 8horseshoe vortex inflow generated from the rudder.

Submarine without fillets

Submarine with fillets

Propeller diameter
Velocity[i] (m/s)
9.5
8.2
6.9
5.6

4.3
3.0

Figure 4. Wake distribution at propeller plane (left) submarine without fillets (right) submarine with fillets

Reference
blade

Blade loading along
the angular position

y

y

z

Ref.
blade

𝜃
z

Ω

: 4th harmonic unsteady source: 8th harmonic unsteady source

Figure 5. Unsteady noise sources of propeller blade induced by non-uniform wake
Figure 6 shows the directivity of the first BPF noise depending on whether the submarine is equipped withthe fillets or not. The receivers of the predicted noise are located on a circle with a radius of 20 m from thecenter of the propeller on the middle plane. The black line represents the overall noise, and the blue and redlines represent the loading and thickness noise, respectively. In the case of overall noise, it can be seen that thesound pressure level (SPL) of first BPF noise is reduced by 5∼12 dB at 0∼60 degrees and 180∼240 degrees
when the fillets are installed. Comparing the analysis results for each type of noise source, it can be seen thatthe thickness noise has relatively little change and thus has less effect, and that the overall noise is mainly
reduced due to the loading noise.

5

CONCLUSIONS

A frequency-domain noise model for predicting BPF noise generated from underwater propellers was developed.
The developed noise prediction model was applied to analyze the noise reduction of the submarine propeller
according to the installation of the fillets. First, through hydrodynamic calculation, when fillets are installedon the front and rear part of the appendages such as sail and rudder of the submarine, the strong adverse
pressure gradients around the appendages are resolved and the generation of unfavorable flows such as HSV is
reduced. Moreover, by reducing the HSV, the distribution of wake flowing into the propeller became uniform,
so unsteady sources generated from the propeller blades were significantly reduced.
By substituting the calculated unsteady source data into the developed noise prediction model, the BPF noise
generated from the submarine propeller was predicted in consideration of the hydrodynamic interaction between
the appendages and the propeller. The prediction of the BPF noise reduction according to the installation of thefillets on the submarine was performed through the developed noise model. In the first BPF, the contribution of
the loading noise was higher than the thickness noise, and the overall noise reduction by 5∼12 dB was shown.
In the second BPF, the contribution of the thickness noise was similar to or stronger than that of the loading
noise, and due to the reduction of thickness noise by about 20 dB, the overall noise was decreased by up to 20

: without fillets: with fillets

Overall noise: without fillets: with fillets

Loading noise: without fillets: with fillets

Thickness noise

Figure 6. Comparison of directivity of 1st BPF noise from submarine with and without fillets (left) overall noise(middle) loading noise (right) thickness noisedB in the range except the axial direction.
In the future, it is expected that the results of this study can be utilized in the development of design
techniques for deriving the acoustically optimized shapes of rudder and sail. Furthermore, an analysis of thechange in acoustic characteristics caused by changing the rudder to an X-shape will be performed.

ACKNOWLEDGEMENTS
This study was funded by the Future Submarine Low Noise Propeller Research Laboratory of Korea ResearchInstitute of Ships and Ocean Engineering supported by Defense Acquisition Program Administration and Agency
for Defense Development.

REFERENCES[1] Devenport, W. J., Simpson, R. L., Dewitz, M. B., Agarwal, N. K. (1992). Effects of a leading-edge fillet
on the flow past an appendage-body junction. AIAA journal, 30(9), 2177-2183.
[2] Zess, G. A., Thole, K. A. (2002). Computational design and experimental evaluation of using a leadingedge fillet on a gas turbine vane. J. Turbomach., 124(2), 167-175.
[3] Toxopeus, S., Kuin, R., Kerkvliet, M., Hoeijmakers, H., Nienhuis, B. (2014, June). Improvement of resistance and wake field of an underwater vehicle by optimising the fin-body junction flow with CFD. In
International Conference on Offshore Mechanics and Arctic Engineering (Vol. 45400, p. V002T08A046).
American Society of Mechanical Engineers.
[4] Liu, Z. H., Xiong, Y., Tu, C. X. (2014). The method to control the submarine horseshoe vortex by breaking
the vortex core. Journal of Hydrodynamics, 26(4), 637-645.
[5] Hanson, D. B. (1980). Helicoidal surface theory for harmonic noise of propellers in the far field. AIAA
journal, 18(10), 1213-1220.
[6] Hanson, D. B. (1983). Compressible helicoidal surface theory for propeller aerodynamics and noise. AIAA
Journal, 21(6), 881-889.
[7] Hanson, D. B. (1985). Noise of counter-rotation propellers. Journal of Aircraft, 22(7), 609-617.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022 in Gyeongju, Korea

ABS-0132

Broadband noise prediction of a pump-jet propeller for submarine
using wall pressure spectrum
Min-Hyeok KIM1, 2; Suk-Yoon HONG1,2; Jee-Hun SONG3; Il-Ryong PARK4; Min-Jae KIM5
1

Department of Naval Architecture and Ocean Engineering, Seoul National University, South Korea
2

3

Institute of Engineering Research, Seoul National University, South Korea

Department of Naval Architecture and Ocean Engineering, Chonnam National University, South Korea
4

Department of Naval Architecture and Ocean Engineering, Dongeui University, South Korea
5

Naval System R&D Institute, Agency for Defense Development, South Korea

ABSTRACT
Since submarines generally operate in non-cavitating conditions and the use of a Pump-Jet Propeller(PJP) instead of a conventional single propeller can decrease tone noises, contributions of mid-to-highfrequency broadband noise to radiation noise become significant. PJP consists of a decelerating duct, afixed stator adjusting flow direction, and a rotating rotor generating flows. In this paper, broadband noisefrom trailing edges was analyzed to predict the radiation noise at multiple observation points, and thecontribution of each component was compared. Since noise sources up to high frequency are obtained
from small eddies in turbulent boundary layers, Wall Pressure Spectrum (WPS) was used with input data
given by Computational Fluid Dynamics (CFD) simulation with Reynolds-averaged NavierStokes(RANS) turbulence model. Thin airfoil theory was used to predict distributions of acousticpressure on blades. Noise radiation from trailing edges to far-field observation points was calculated byapplying duct green’s function through PJP and free-field green’s function after its exit. By comparing
the contribution, it can be identified which parts need to be redesigned to reduce the noise, anddecreasing the radiation noise in all directions can be achieved.
Keywords: Pump-jet propeller, Broadband noise, Wall pressure spectrum

1. INTRODUCTION
An important performance of a submarine is stealth, and the underwater radiation noise must be
reduced so that enemy cannot detect it. Most of the noise is generated by thrusters, and PJPs are
introduced instead of conventional single propellers to reduce it. As single propellers have been used
for decades, the mechanisms of radiation noise have been elucidated, and various design methods
have been proposed to reduce noise. However, since PJPs are a more complex structure than single
propellers, diverse noise sources exist, and accordingly, design methods are required.
In general, the noise generated by propellers can be divided into tone noise, broadband noise, andcavitation noise. However, submarines are in non-cavitation operating conditions, and radiation of
low-frequency tone noises such as BPF noises can be blocked by combinations of the number of bladesof a rotor and a stator or applying a duct liner. Therefore, the broadband noise generated by turbulence
is important to reduce underwater radiation noise for the design of PJPs. PJPs consist of a rotor, astator, and a duct. A rotor that creates the flow experiences a high -velocity flow due to rotation and isa major noise source because it is under strong pressure on the blade surface. A stator serves to adjust
the flow in front or behind a rotor and is a relatively weak noise source due to a lower velocity flow
and weak pressure compared to the rotor. However, wake interactions between a rotor and a statorbecome an additional noise source. A duct in PJPs for submarines is designed as a decelerating duct
to improve noise performance, and pressure can be intense depending on the incidence angle.
Although a duct does not experience a high-velocity flow, it becomes a significant noise source due
to its wide cross-sectional area.
All components of PJPs need to be considered for noise prediction. Since normal vectors of blades
and a duct surface differ by about 90 degrees, the primary component of the noise can vary dependingon observation angles. This study predicted the broadband noise from the trailing edges, which isdominant in mid-to-high frequency, at various observation angles. The contribution of eachcomponent was compared using its radiation directivity. RANS CFD was performed, and wall pressure
spectrum and thin airfoil theory were used to obtain noise sources. Duct green's function in the duct
and free-field green's function outside the duct was applied to predict far-field radiation noise.

2. THEORETICAL BACKGROUND
2.1 Theory for Noise using Green’s Function
Noise generated from PJPs can be evaluated by Lighthill’s equation as shown in Equation (1).
𝑇𝑝(𝑥⃗, 𝑡) = ∫ ∫𝜌0 𝑉𝑗 𝑛𝑗 (𝑦⃗, 𝜏)−𝑇 𝑆(𝜏)𝑇+∫ ∫𝑝𝑖𝑗 𝑛𝑗 (𝑦⃗, 𝜏)−𝑇 𝑆(𝜏)𝑇+∫ ∫𝑇𝑖𝑗 (𝑦⃗, 𝜏)−𝑇 𝑉(𝜏)𝐷𝐺(𝑦⃗, 𝜏|𝑥⃗, 𝑡)𝑑𝑆(𝑦⃗)𝑑𝜏𝐷𝜏𝜕𝐺(𝑦⃗, 𝜏|𝑥⃗, 𝑡)𝑑𝑆(𝑦⃗)𝑑𝜏𝜕𝑦𝑖(1)

𝜕 2 𝐺(𝑦⃗, 𝜏|𝑥⃗, 𝑡)𝑑𝑉(𝑦⃗)𝑑𝜏𝜕𝑦𝑖 𝜕𝑦𝑗where G is green’s function, an observer is at 𝑥⃗, 𝑡 a source is at 𝑦⃗, 𝜏. Three integrals representmonopole, dipole, and quadrupole noise sources, respectively. Among them, the noise source that
contributes the most to the broadband noise in the far field is the loading noise expressed by the dipole.
The others have lower magnitude or cannot propagate far. Noise can be calculated using Equation (1)and green's function according to boundary conditions. Free-field green's function and duct green's
function are used for PJPs and each function is expressed as Equation. (2), (3).
(2)

𝐺(𝑥⃗, 𝑡|𝑦⃗, 𝜏) = 𝑒 𝑖𝑘|𝑥⃗−𝑦⃗⃗| /4𝜋|𝑥⃗ − 𝑦⃗|where 𝑘 is wave number.

𝐺(𝑥⃗, 𝑡|𝑦⃗, 𝜏) =

𝑖 ∞
1
∫ ∑
𝜓 (𝛼 𝑟)𝜓𝑚 (𝛼𝑚𝑣 𝑟0 )4𝜋 −∞Λ mv 𝑘𝑚𝑣 𝑚 𝑚𝑣
𝑚,𝑣

(3)

2

× 𝑒 −𝑖𝜔(𝑡−𝜏)+𝑖𝑚(𝜙−𝜙0)−𝑖(𝑀𝑘0 ±𝑘𝑚𝑣)(𝑧−𝑧0 )/𝛽 𝑑𝜔where 𝛼𝑚𝑣 is zeros of a Bessel function, 𝜓. A source and an observer are expressed as cylindricalcoordinate system as 𝑦⃗ = (𝑟0 , 𝜙0 , 𝜏), 𝑥⃗ = (𝑟, 𝜙, 𝑡). An axial wave number is 𝑘𝑚𝑣 , and Λ mv satisfies
following Equation (4).
𝑟

𝑐
2 (𝛼
Λ mv = 𝜋[(𝑟 2 − (𝑚/𝛼𝑚𝑣 )2 )𝜓𝑚𝑚𝑣 𝑟)]𝑟ℎ(4)

In thin airfoil theory, the dipole noise source is replaced by pressure jump across the blades. Noise in
free-field can be calculated by Equation (5).

1 𝑇 𝑖𝜔(𝑥𝑗 − 𝑦𝑗 )∫∫ 𝑛 (𝜏)Δ𝑝(𝑦⃗, 𝜏)𝑑𝑆(𝜏) 𝑒 𝑖𝜔(𝜏+|𝑥⃗−𝑦⃗⃗|/𝑐∞ ) 𝑑𝜏
2𝜋 −𝑇 4𝜋𝑐∞ |𝑥⃗ − 𝑦⃗|2 𝑆(𝜏) 𝑗𝑝(𝑥⃗, 𝜔) =(5)

Noise in duct can be calculated by Equation (6), (7).
∞∞𝑝(𝑥⃗, 𝜔) = ∑ ∑ 𝑝𝑚𝑣 (𝜔)𝜓𝑚 (𝛼𝑚𝑣 𝑟)𝑒 𝑖𝑚𝜙− 𝑖(𝑀𝑘0 ±𝑘𝑚𝑣 )𝑧/𝛽2(6)𝑚=−∞ 𝑣=0𝑇

𝑚𝑠𝑖𝑛(𝜃0 ) (𝑀𝑘0 ± 𝑘𝑚𝑣 ) 𝑐𝑜𝑠(𝜃0 )
(
−
)
𝑟0
𝛽2
−𝑇 𝑆(𝜏)𝑝𝑚𝑣 = ∫ ∫(7)𝑖(𝑀𝑘0 ±𝑘𝑚𝑣 )𝑧0𝜓𝑚 (𝛼𝑚𝑣 𝑟0 )𝑖𝜔𝜏−𝑖𝑚𝜙0 +𝛽2×𝛥𝑝𝑒𝑑𝑆(𝑦⃗)dτ
4𝜋Λ 𝑚𝑣 𝑘𝑚𝑣

2.2 Broadband Noise Sources
Broadband noise from trailing edges is generally dominant in the mid -to-high frequency and isgenerated by small eddies. However, since such a noise source cannot be obtained from CFD datausing the turbulence model, the wall pressure spectrum was used instead. The thin airfoil theory first
derived by Amiet determines the pressure distributions on the blades and is improved by Roger andMoreau. Equation (8) shows the theory, and transfer function 𝑔 means the pressure distributions.
(8)

𝛥𝑃(𝑥1 , 𝜔) = 4𝜋𝐴(𝜔)𝑒 𝑖𝜙(𝜔) 𝑔(𝑥1 , 𝑘𝑐 , 0)

where 𝑘𝑐 = 𝜔/𝑈𝑐 is convection wave number, and 𝜙 is random phase distributed on [0, 2π]. 𝐴 isthe amplitude of noise sources and is determined from wall pressure spectrum as Equation (9).
1/2

(8)

𝐴 = [2𝑆𝑞𝑞 (𝜔, 0)𝑙2 (𝜔)Δ𝜔]

where 𝑆𝑞𝑞 (𝜔, 0) is the spanwise wall pressure cross-spectrum and 𝑙2 is the spanwise correlation
length. The accuracy of the wall pressure spectrum models varies according to the pressure gradientson the surface. The Lee model was selected in the adverse pressure gradients, and the Hu model was
selected in the favorable pressure gradients.

3. BROADBAND NOISE PREDICTION OF A PJP
3.1 Evaluation of Broadband Noise Sources
In this section, numerical simulation using RANS CFD is performed to extract input variables ofwall pressure spectrum. The specifications of the Suboff submarine and the PJP are shown in Table 1.
Table 1 - Specifications of submarine and PJP
Description

Dimension

SymbolSuboffLength overall

4m

L

PJP

Blade number

7

B

Vane number

11

V

Diamenter

0.245mD

Self-propulsion is at (ship speed, rotation speed) = (9.477m/s, 30.896rps). Figure 1 and 2 showgeometries and meshes of the submarine and the PJP.

Figure 1 - Geometries of submarine(left) and PJP(right)

Figure 2 - Meshes of submarine(top) and PJP(bottom)
Pressure contour of PJP is shown in Figure 3. They are the PJP, only rotor and stator, pressure side ofa rotor blade and suction side of a rotor blade from left to right.

Figure 3 - Pressure contour of PJP
Input variables of wall pressure spectrum are flow velocity, pressure gradients on the surfaces, A local
minimum point of the pressure along the line normal to the surfaces was used to extract boundary
layer thickness in Figure 4. The boundary layer thickness of the rotor are the larges followed by theduct and the stator. Using the Equation (8) and calculation of the wall pressure spectrum, noise sources
can be obtained.

Figure 4 - Boundary layer thickness of PJP components;
roto(top), stator(middle), duct(bottom)
3.2 Prediction of Far-field Broadband noise
Noise sources and corresponding broadband noise from rotor, stator and duct can be calculated by
Equation (5) ~ (8). Since broadband noise has a wide frequency band and fluctuates, it is necessary
to specify a representative value to compare the contribution between components. In this study, theSound Pressure Level(SPL) filtered by 1/3 octave band are compared at 1k, 2.5k, 5k, and 10k at
multiple observation angles. The observation points form a quarter circle at a distance of 10D fromthe center of the duct exit, and the noise predictions are shown as SPL in Figure 5.

Figure 5 - Comparison of broadband noise for PJP components at multiple observation angle as SPL;
at 1kHz(top left corner), 2.5kHz(top right corner), 5kHz(bottom left corner), 10kHz(bottom right corner)
The noise from the rotor and the duct determines the total noise, and the contribution of the stator
is insignificant. The contribution of the rotor and duct changes according to the frequency andobservation angle. At 1 kHz, the SPL of the rotor is more considerable near 0 degrees. However, the
SPL of the duct is more considerable near 90 degrees. Around 90 degrees is where noise from therotor generated in the duct does not radiate well. On the other hand, it is a location where the noise of
the duct radiates efficiently. This tendency appears until 5 kHz. However, at 10 kHz, the noise of therotor is dominant, even near 90 degrees. The reason is that the turbulence mainly has a low -frequency
noise source since it is generated at low speed and weak wall shear stress. From the results, to reducethe broadband noise in the mid-to-high frequency bands of PJPs, it is necessary to design a rotor orduct which can suppress the generation of turbulence around it. Since major noise sources change
depending on the observation angle and frequency band that require noise reduction, the desi gn of
PJPs must consider them. Also, a contribution tendency at a frequency band is expected to alterdepending on the dimension of PJPs.

4. CONCLUSIONS
Unlike the conventional single propellers, the PJPs generate noise from three structures: a rotor, astator, and a duct. In order to reduce the noise of PJP in the mid -to-high frequency, it is necessary to
determine which component has the most outstanding contribution. Using Lighthill's equation, green's
function, and thin airfoil theory, broadband noise from the trailing edges generated in and outside theduct was calculated. When comparing the noise filtered by 1/3 octave band at several observation
points, the contribution of the PJP component was changed according to observation angle andfrequency band. This result makes it possible to determine the components that need to be changed toreduce the noise of PJPs.

ACKNOWLEDGEMENTS
This study was funded by the Future Submarine Low Noise Propeller Research Laboratory ofKorea Research Institute of Ships and Ocean Engineering supported by Defense Acquisition Program
Administration and Agency for Defense Development.

REFERENCES
1. Glegg S. A., and Devenport W. Aeroacoustics of low Mach number flows: fundamentals, analysis, andmeasurement. Academic Press; 2017.
2. M. E. Goldstein, Aeroacoustics. New York; 1976.
3. J. Casper, and F. Farassat, Broadband trailing edge noise predictions in the time domain. Journal of Soundand Vibration. 2004;271(1-2), 159-176.
4. W. S. Choi, S. Y. Hong, J. H. Song, H. W. Kwon, I. R. Park, H. S. Seol, and M. J. Kim, Time domain
broadband noise predictions for non-cavitating marine propellers with wall pressure spectrum models,International Journal of Naval Architecture and Ocean Engineering. 2021; 13, 75-85.
5. S. Lee and J. G. Shum, Prediction of airfoil trailing-edge noise using empirical wall-pressure spectrum
models. AIAA Journal. 2019;57(3), 888-897.
6. N. Hu and M. Herr, Characteristics of wall pressure fluctuations for a flat plate turbulent boundary layer
with pressure gradients. AIAA/CEAS 22nd Aeroacoustics Conference. AIAA Paper. 2016;2016-2749.
7. M. Roger and M. Stéphane, Back-scattering correction and further extensions of Amiet's trailing-edge
noise model. Part 1: theory. Journal of Sound and vibration. 2005;286(3), 477-506.
8. R. K. Amiet, Noise due to turbulent flow past a trailing edge. Journal of sound and vibration. 1976;47(3),387-393.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022 in Gyeongju, Korea

ABS-0134

Propeller CIS Estimation by Bubble Dynamics
for Naval Surface Ship
Seung-Jin JEONG1,2; Suk-Yoon HONG1,2; Jee-Hun SONG3
1

Department of Naval Architecture and Ocean Engineering, Seoul National University, South Korea
2

3

Institute of Engineering Research, Seoul National University, South Korea

Department of Naval Architecture and Ocean Engineering, Chonnam National University, South Korea

ABSTRACT
Cavitation occurs with an increase in hull vibration, a decrease in propulsion performance, and an increasein radiated noise. Since these phenomena are especially fatal to naval ships such as fleets and submarines,
each country's navy has introduced and managed a propeller performance index called Cavitation Inception
Speed (CIS).
In this paper, the surface ship's propeller Tip Vortex Cavitation (TVC) was analyzed using bubble dynamics,
and CIS was presented through numerical analysis in terms of noise, the most prominent feature of cavitation
inception. The behavior of cavitation is simulated with bubble dynamics analysis for the cavitation nucleus,
and the input data of the analysis is obtained from computational fluid dynamics (CFD) simulation. The noise
value from each nucleus was calculated by modeling the derived bubble behavior with a monopole. Whenthe cavitation nucleus grows into a cavitation bubble, additional impulse noise is generated due to theimplosion as the bubble contracts, which can be used as a CIS determination criterion. Bubble analysis andnoise analysis were performed under various cavitation conditions to identify the propeller CIS of the surface
ship using inflection of noise increase tendency.
Keywords: Naval Ship, Propeller, CIS

1. INTRODUCTION
Cavitation refers to a phenomenon in which air bubbles are generated due to a drop in pressure
inside a liquid fluid and occurs mainly when fine air bubbles pass through the low -pressure area
caused by the influence of high-speed vehicles. Cavitation can have fatal consequences for naval
vessels because it is accompanied by phenomena such as degradation of propulsion performance,
propeller damage, and in particular increased noise and vibration of ships. The exposure of noise
information from the propeller may expose the operating environment to the enemy, causing damage
to the entire navy. Therefore, it is necessary to predict the onset of cavitation, and the Cavitation
Inception Speed (CIS) is set and managed as an essential evaluation indica tor of naval vessel
performance worldwide.
Among the various types of cavitation originating from propellers, tip vortex cavitation (TVC)
generally tends to occur first. As a result, navies in each country have conducted many studies topredict its inception speed. In many studies, CIS has been visually judged, and a method of detecting
the moment when cavitation bubbles were observed at the blade's tip has been utilized. (1 3, 20).
However, a feature that appears before the visual generation of bubbl es in TVC generation is theincrease in noise. This noise occurs on acoustic measurements even though the bubble is not visuallyobserved. This is because the noise caused by the cavitation bubble is the largest at the maximum
contraction point, not the bubble's expansion (7). The computational fluid dynamics (CFD) method
has also been studied a lot. Still, there is a limit to distinguishing singularities due to noise as it isbiased toward specifying flow characteristics (1, 22).
Therefore, in this study, CIS prediction was conducted by adding a procedure that can analyze
noise characteristics by cavitation using CFD analysis data. Many researchers have studied modelingnoise sources by cavitation bubbles and predicting behavior using bubble dynamics theory. Eachbubble has been modeled primarily in the form of a monopole and has been used to predict cavitation

in underwater wing sections. (8, 9, 16). Based on these theories, Jeong et al. (10, 11) established aprocedure for determining CIS based on the inflection of noise increase trend and used it forunderwater elliptic wings. In addition, the established procedures were applied to submarine
propellers of various geometries to predict each CIS.

2. THEORY AND PROCEDURES FOR TVC CIS ESTIMATION
2.1 Bubble Dynamics Equations
The bubble dynamics theory was used to predict the behavior of the cavitation nucleus scatteredin the flow field. Bubble dynamics is a governing equation that expresses the behavior of external
forces such as pressure, pressure gradient, and velocity acting on a bubble. Estimating the size of
bubbles is performed using the equation that models the behavior of spherical objects in waterproposed by Rayleigh (19), and Plesset (17, 18), as shown in Equation (1).
3 2
1
𝑅0 3𝛾
2𝑆 4𝜇
̈
̇
𝑅𝑅 + 𝑅 =(𝑝𝑣 + 𝑝𝑔0 ( ) − 𝑝∞ −
−
𝑅̇ )
2
𝜌𝑤
𝑅
𝑅
𝑅

(1)

where R indicates the size of the bubble, and the dot notation means time derivative. The right-handside of the equation in turn means vapor pressure (p v), gas pressure (p g) in bubbles, external pressure(pv ), surface tension (S), and viscosity (μ). The ρw indicates the density of water, each zero subscript
means the value of the initial state, γ is the polytropic constant of the gas, ∞ subscript means the value
at the far-field.
The positions of each bubble over time can be obtained from the bubble motion equation. Maxeyand Riley (14) introduced a motion equation considering body forces such as gravity, buoyancy, drag,and pressure gradient acting on the spherical body in water. The bubble motion equation used is asfollows Equation (2).

𝜌𝑏 𝑉𝑏

⃑⃑⃑⃑𝑏
⃑ 𝑑𝑈
⃑⃑⃑⃑𝑏
𝑑𝑈
1
1
𝑑𝑈
⃑ −𝑈
⃑⃑⃑⃑𝑏 )|𝑈⃑ −𝑈⃑⃑⃑⃑𝑏 | + 𝜌𝑤 𝑉𝑏 (= 𝑉𝑏 (𝜌𝑏 − 𝜌𝑤 )𝑔 − 𝑉𝑏 𝛻𝑝 + 𝜌𝑤 𝐴𝑏 𝐶𝐷 (𝑈
−
)
𝑑𝑡
2
2
𝑑𝑡
𝑑𝑡

(2)

The terms on the right side of the equation in order mean buoyancy and gravity, a force due topressure gradient, drag force, and added mass by liquid. The drag coefficient (CD ) included in the dragforce term used the formula of Haberman and Morton (6), as shown in Equation (3), Reb in the formula
represents the Reynolds number for the bubble radius, and ν represents the dynamic viscosity of water.
In addition, ρ denotes the density, V denotes the volume of bubbles, U denotes the velocity of flow
and bubbles, g denotes the gravitational acceleration, ∆p means the pressure gradient, and A
indicates the cross-section of bubbles. The subscripts b and w refer to the properties of air and water,
respectively.
𝐶𝐷 =24(1 + 0.197𝑅𝑒𝑏 0.63 + 2.6 × 10−4 × 𝑅𝑒𝑏 1.38 )
𝑅𝑒𝑏

(3)

2𝑅
⃑ −𝑈
⃑⃑⃑⃑𝑏 |
|𝑈
𝜐

(4)

𝑅𝑒𝑏 =

The bubble motion equation receives the pressure, pressure gradient, and speed fields of the sternwake and outputs the acceleration value of each cavitation bubble over time. The velocity andcoordinates of the bubbles can be obtained by integrating the calculated acceleration. In this way, theLagrange approach, which tracks each bubble behavior over time using the Rayleigh-Plesset equationand the bubble motion equation, was used for cavitation analysis, which is very advantageous forpredicting TVC occurring in a narrow area.
The behavior of the bubble surface causes noise from the bubble. Therefore, the vibration of thespherical bubble surface can be expressed by modeling each bubble as a monopole (w). The magnitudeof the generated acoustic pressure can be described as shown in Equation (5) below.

𝑝`(𝑡) =𝜌𝑤 𝑑 2 𝑉𝑏
𝑅= 𝜌𝐿 (2𝑅̇ 2 + 𝑅𝑅̈ )2
4𝜋𝑟 𝑑𝑡𝑟(5)

In the formula, R represents the radius of bubbles derived from the Rayleigh-Plesset equation, andthe dot notation in the term represents a time derivative. In addition, r represents the distance fromthe current location of the bubble to the receiver and is calculated using the coordinates derived fromthe bubble motion equation.
2.2 Cavitation number conditions
The cavitation number is a non-dimensional number for the ratio of pressure to inertial force andhelps evaluate whether cavitation has occurred (3). The smaller the cavitation number, that is, when
the pressure term is small, or the inertial force term is large, it can be considered cavitation occurs
more. The cavitation number in which the rotational speed of the propeller is considered in the inertial
force term can be expressed as shown in Equation (6) below, and J in Equation (7) means the advance
ratio of the propeller.
𝜎𝑖 =𝑃𝑎𝑚𝑏𝑖𝑒𝑛𝑡 − 𝑝𝑣=
0.5𝜌𝑤 {𝑈𝑖𝑛𝑓𝑙𝑜𝑤 2 + (0.7𝜋𝑛𝐷)2 }𝐽=

1𝑃𝑎𝑚𝑏𝑖𝑒𝑛𝑡 − 𝑝𝑣
20.7𝜋
0.5𝜌𝑤 {1 + (𝐽 ) }𝑈𝑖𝑛𝑓𝑙𝑜𝑤 2

𝑈𝑖𝑛𝑓𝑙𝑜𝑤
𝑛𝐷

(6)

(7)

where pv means vapor pressure, ρ w means the density of water, U means speed value of inflow, Dmeans diameter of the propeller, n means rotation speed of the propeller.

3. Surface ship propeller TVC Estimation
3.1 Naval surface ship flow fields
The data required to perform the cavitation analysis of the propeller are the pressure, speed, andpressure gradient of the flow-field around the propeller. Such data can be obtained throughComputational Fluid Dynamics (CFD) analysis.
The CFD analysis was performed on surface ship alone, and the reliability of the analysis was
confirmed by comparing them with reference results. The model used in the study is ONR
Tumblehome, and the geometry and specifications are shown in Table 1 and Figure 1 below.
Table 1 - Specifications of surface ship models
ValuesONR Tumblehome

Lwl (m)3.147

Bwl (m)

0.384

T (m)

0.112

Displacement (m3)0.07326

Figure 1 - Geometry of ONR Tumblehome
The analysis settings of this study are shown in Table 2. The results were verified by comparing
the hull resistance values and the formed Kelvin wave patterns with other literature's analysis andexperimental values. The resistance and wave pattern of ONRT were verified using the results of Cook(4) and Delen (5).
Table 2 - CFD analysis settings
Governing equations

RANS

Turbulence model

k-w SST

CFD time step

0.0001 sec

Table 3 - Resistance values of ONRT
ONRTResistance (N)Difference (%)

Fn = 0.30
EFD

CFD

11.08

11.06
0.18

Figure 2 - Wave pattern by ONR Tumblehome (Fn = 0.30)
The propellers attached to the surface ship are the ONR Tumblehome’s propellers. To verify thereliability of the propeller CFD analysis, the analysis was conducted in the Propeller Open Water(POW) state. The values of the three propulsion coefficients represented by the thrust coefficient,torque coefficient, and propulsion efficiency were derived and compared with the experimental values(23).

Figure 3 - Geometry of ONR Tumblehome propeller
Table 4 - Specifications of ONRT propeller
Value
Propeller diameter (m)Propeller center / Lwl

0.1066Long

0.9267

Lateral0.02661

Vertical

0.03565

Propeller shaft angle (deg)5

Figure 4 - Propulsion coefficients of ONRT propeller
3.2 Cavitation nuclei distributions
In the water, there are inherently invisible fine bubbles, which are called cavitation nuclei. These
cavitation nuclei grow into visible cavitation bubbles as they pass through the low-pressure zone
formed by high-speed underwater motion. The density of cavitation nuclei varies greatly dependingon the environment. The higher the density, the weaker the tensile strength of the liquid, and t hus
more cavitation. Therefore, many researchers have conducted many studies to measure the density ofcavitation nuclei (12, 15), and experiments on the effect of cavitation inception according to thedensity have also been conducted (21). The density of each cavitation nuclei shown in the studies canbe roughly expressed as shown in Equation (8) below.

(8)𝑙𝑜𝑔10 𝑁 = 𝐶 − 3 𝑙𝑜𝑔10 2𝑅

where R means the initial radius of the nucleus, N indicates the total number of nuclei per 10 ml
corresponding to the size mentioned above, R, and C means the water quality coefficient. This study,
6.0 was used as the coefficient value for the freshwater conditions.
The smaller the size, the more present; the larger the size, the fewer the number. In addition, thesmaller the initial size of the nucleus, the lower the cavitation frequency due to factors such as surface
tension, so it is important to select an appropriate size distribution for analysis. In this study, basedon the cavitation nuclei density distribution function provided by Equation (8), the initial size was set
to have a continuous distribution, as shown in Figure 5. For cavitation analysis, these cavitation nuclei
were disposed on the tip vortex field calculated by CFD.

Figure 5 - Cavitation nuclei number distribution by size

3.3 Initial hydrostatics conditions
As an initial condition for cavitation analysis, in addition to the initial coordinates, the hydrostaticpressure input to the Rayleigh-Plesset equation must be input. The hydrostatic pressure condition isrepresented by each cavitation number condition, as shown in Equation (6). If the propeller's advance
ratio and the rotational speed are fixed in the cavitation number equation, the following relat ionships
between the hydrostatic pressure and the inflow speed are established.
𝜎2
𝜎1

=

𝑃2 − 𝑝𝑣
𝑃1 − 𝑝𝑣(when Uinflow is fixed) or

𝜎2
𝜎1

=

𝑈1 2
𝑈2 2

(when Pambient is fixed)(9)

As shown in Equation (9), each hydrostatic pressure condition and speed condition are mutuallycompatible under specific conditions. The cavitation analyses were performed by varying thecavitation number conditions by fixing 10 knots of the speed condition in CFD and adjusting thehydrostatic pressure. The speed condition corresponding to each cavitation number may be expressedby assuming atmospheric pressure.
The bubble dynamics equation was numerically calculated about various hydrostatic pressure
conditions and solved using the 4th Runge-Kutta method. The time steps used for bubble dynamics
analysis are 2µs, which can be adaptively divided into smaller intervals as the speed of the bubble
surface increases.
3.4 CIS estimation about surface ship propeller
Figure 6 shows the magnitude of the cavitation bubble noise generated by the propeller under eachcondition by summing the decibels in a specific frequency band. Considering the retarded time causedby the distance from the bubble to the receiver, all acoustic pressures at the receiver position wereadded.

Figure 6 - Surface ship propeller CIS estimation

In the trend of propeller noise shown in the analysis, white noise can be seen under high hydrostaticpressure conditions. As the hydrostatic pressure decreases, additional impact noise is generated. This
study judged that tip vortex cavitation occurred for the first time when the noise tendency changed
significantly, such as in the red shaded area in Figure 6. As the hydrostatic pre ssure conditions change,
it can be seen that a noise source that did not exist before was added, and in this analysis, it can beconsidered to be caused by cavitation bubbles.

4. CONCLUSIONSIn this study, the inception of TVC, which is a problem in many naval vessels, especially surface
ship propellers, was predicted using noise analysis based on bubble dynamics. It is estimated using
the most distinguished feature before and after propeller CIS, the increasing trend of noise.
To realize the cavitation behavior, cavitation nuclei were used, and the bubble dynamics equation
was applied. The flow fields required for bubble dynamics analysis include pressure, velocity, andpressure gradient, and these data were derived through CFD analysis. Hydrostatic pressure conditions
were adjusted to set various cavitation number conditions, and CIS was predicted by comparing noiselevels generated in each condition. The point where the trend of increasing cavitation noise changes
before and after a certain number of cavitation conditions was identified and designated as the CIS of
the surface ship propeller.
In future work, the CIS prediction of actual large naval vessel propellers will be carried out basedon the procedures and results in the benchmark ship model. These studies are expected to significantly
contribute to predicting CIS in the design stage of naval ship propellers.

ACKNOWLEDGEMENTS
This study was funded by the Future Submarine Low Noise Propeller Research Laboratory of
Korea Research Institute of Ships and Ocean Engineering supported by Defense Acquisition Program
Administration and Agency for Defense Development.

REFERENCES
1. Asnaghi A, Svennberg U, Bensow RE. Numerical and experimental analysis of cavitation inception
behaviour for high-skewed low-noise propellers. Applied Ocean Research. 2018;79:197-214.
2. Blake WK. Mechanics of flow-induced sound and vibration, volume 1: General concepts and elementarysources: Academic press; 1986.
3. Carlton J. Marine propellers and propulsion: Butterworth-Heinemann; 2018.

4. Cook SS. Effects of headwinds on towing tank resistance and PMM tests for ONR Tumblehome: The
University of Iowa; 2011.
5. Delen C, Can U, Bal S. Prediction of resistance and self-propulsion characteristics of a full-scale naval
ship by CFD-based GEOSIM method. Journal of Ship Research. 2021;65(04):346-61.
6. Haberman WL, Morton R. An experimental investigation of the drag and shape of air bubbles rising invarious liquids. David Taylor Model Basin Washington DC; 1953.
7. Higuchi H, Arndt R, Rogers M. Characteristics of tip vortex cavitation noise. Journal of Fluids
Engineering. 1989;114(4):495-501.
8. Hsiao C-T, Chahine GL, editors. Prediction of vortex cavitation inception using coupled spherical andnon-spherical models and UnRANS computations. Proceedings of 24th Symposium on Naval
Hydrodynamics, Fukuoka, Japan; 2002.
9. Hsiao C-T, Chahine GL. Scaling of tip vortex cavitation inception noise with a bubble dynamics modelaccounting for nuclei size distribution. Journal of Fluids Engineering. 2005;127(1):55-65.
10. Jeong S-J, Hong S-Y, Song J-H, Kwon H-W, Seol H-S. Establishment of cavitation inception speed
judgment criteria by cavitation noise analysis for underwater vehicles. Proceedings of the Institution of
Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment. 2021;235(2):54657.
11. Jeong S-J, Hong S-Y, Song J-H, Kwon H-W, Seol H-S. Numerical method to determine the cavitation
inception speed of a submarine propeller based on the noise obtained from bubble dynamics. Ocean
Engineering. 2022;245:110464.
12. Kamiirisa H, editor The effect of water quality characteristics on cavitation noise. Fourth International
Symposium on Cavitation, California Institute of Technology, Pasadena, CA USA; 2001.
13. Keller AP, editor Cavitation scale effects-empirically found relations and the correlation of cavitation
number and hydrodynamic coefficients. Fourth International Symposium on Cavitation, California
Institute of Technology, Pasadena, CA USA; 2001.
14. Maxey MR, Riley JJ. Equation of motion for a small rigid sphere in a nonuniform flow. The Physics of
Fluids. 1983;26(4):883-9.
15. O’Hern T, d’Agostino L, Acosta A. Comparison of holographic and Coulter Counter measurements ofcavitation nuclei in the ocean. Journal of Fluids Engineering. 1988;110(2):200-7.
16. Park K, Seol H, Choi W, Lee S. Numerical prediction of tip vortex cavitation behavior and noise
considering nuclei size and distribution. Applied Acoustics. 2009;70(5):674-80.
17. Plesset MS. The dynamics of cavitation bubbles. Journal of Applied Mechanics. 1949;16:277-82.
18. Plesset MS, Prosperetti A. Bubble dynamics and cavitation. Annual Review of Fluid Mechanics.
1977;9(1):145-85.
19. Rayleigh L. On the pressure developed in a liquid during the collapse of a spherical cavity. Philosophical
Magazine Series 6. 1917;34:94-8.
20. Shen YT, Gowing S, Jessup S. Tip vortex cavitation inception scaling for high Reynolds number
applications. Journal of Fluids Engineering. 2009;131(7).
21. Song M, Xu L, Peng X, Tang D. An acoustic approach to determine tip vortex cavitation inception for an
elliptical hydrofoil considering nuclei-seeding. International Journal of Multiphase Flow. 2017;90:79-87.
22. Yilmaz N, Aktas B, Atlar M, Fitzsimmons PA, Felli M. An experimental and numerical investigation ofpropeller-rudder-hull interaction in the presence of tip vortex cavitation (TVC). Ocean Engineering.
2020;216:108024.
23. A workshop on CFD in ship hydrodynamics, 2015. ONR Tumblehome [Internet]. NMRI (Japan);[updated 2021 May 18; cited 2022 Aug 10]. Available from: https://t2015.nmri.go.jp/onrt.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022 in Gyeongju, Korea
ABS-0158

Experimental and Numerical Advances in Underwater Radiated
Noise Prediction of Cavitating Propeller-Hull Combinations
Julian KIMMERL1; Paul MERTES2; Vladimir KRASILNIKOV3; Kourosh KOUSHAN3; Luca
SAVIO3; Mario FELLI4; Moustafa ABDEL-MAKSOUD5; Nils REICHSTEIN6
1
2

Hydrodynamics & Propeller Design, SCHOTTEL GmbH, Germany

Technical Support Navy & Governmental, SCHOTTEL GmbH, Germany
3

4

Dept. of Ships and Ocean Structures, SINTEF Ocean, Norway

Hydrodynamics and Hydroacoustics Dept., Institute of Marine Engineering (INM) – National Research Council(CNR), Italy5

Institute for Fluid Dynamics and Ship Theory, Hamburg University of Technology (TUHH), Germany
6

Strength, Vibration, Acoustics and Shock, Fr. Lürssen Werft GmbH & Co. KG, Germany

ABSTRACT
Propeller induced cavitation is the primary underwater radiated noise source of motorized shipping activities,
which coincides with acoustic frequencies utilized by marine life and may therefore have negative impacts
on the ecosystem. This paper is the conclusion of the research project ProNoVi introduced at ICA2019 andpresents the final results of both experimental and numerical campaigns on a high-level for all participants.
While propulsion related phenomena are analyzed based on evaluation of high-speed recordings, the focus
lies on model and full scale comparisons of acoustic measurements with pressure pick-ups and hydrophones
in the far-field. Accompanying simulations with active phase transition are undertaken, by employing highfidelity CFD methods with RANS and scale resolved DES or LES turbulence modelling. For different
methods and setups, the emitted noise from the propeller and its slipstream, where induced vorticity andcavitation-dynamics play an important role, are compared for an openwater propeller case and several
propeller-hull combinations. The analysis of these workflows on real propeller-ship combinations reveal
adequate results, regarding comparability and reproducibility between different experimental and numericalsetups and point to future opportunities for the improvement of accurate underwater noise predictions whilesaving numerical and experimental resources.
Keywords: Underwater radiated noise, Marine propeller, Cavitation, CFD, Experiment

1. INTRODUCTION
1.1 URN as Environmental Issue
The spectral background underwater noise characteristics in the earth’s oceans are primarily
affected by anthropogenic noise due to shipping activities in the medium frequency ranges. Oceanic
shipping increases the amplitudes of the medium frequency bands between 10Hz and 1000Hz up to
30dB (1). In general, commercial shipping is, depending on regional circumstances, the dominating
part of the underwater overall noise levels, although it has to be considered that acoustic sensitivityof distinct species may depend on season and frequency range. An overlap between typical shipping
noise and frequencies required for communication, as well as effective predator-prey interaction, isverified, e.g. for the species Catacea (2), Testudines (3) and Elasmobranchii (4). Due to the long lifespan of some of the affected species, the changes in the background noise level occurred in an
evolutionary neglectable timeframe, which may lead to adverse effects on their natural behavior. This
could lead to significant detriments on their life strategies, possibly leading to extinction of species,
1

jkimmerl@schottel.dewhich is cause for the inclusion in some regulatory bodies’ rules and guidelines, such as the EUcommission and the IMO (5). In some cases, these are translated to a local level by regional
regulations with operational implications for the industry, e.g. as implemented by the Port of
Vancouver (6).
To attack the problem effectively, shipping noises require to be differentiated between its sources
and their corresponding frequency ranges, with multiple acoustic emitters on vessels such as
propulsion, engines, gear boxes, pumps and hydraulic aggregates. The most important noise source
over a wide frequency range is the propulsion, once the vessel speed for onset of cavitation is exceededor when operated in off-design conditions, as the imploding large sheet and vortex cavity regions andthe separating single bubbles are the main contributors to broadband noise. Propulsion devices may
be studied individually, however, in reality they are part of a complex system consisting of the ship’s
hull, which affects the inflow and generally the turbulent flow field in which the propulsor is operating,and some form of rudder instrumentation, which typically operates behind the propulsor, due toincreased steering forces for this position and is affected by the highly turbulent propeller slipstream.
For a recent overview of the state of the art see Kimmerl or Krasilnikov (7,8).
1.2 ProNoVi Project
The project ProNoVi - “Analysis Methods and Design Measures for the Reduction of Noise andVibration Induced by Marine Propellers”, as part of the EU-commissions MarTERA ERA-NET cofund,investigates the effects of the aforementioned interactions occurring for a propeller operating inbehind ship condition on the acoustic emissions and aims to develop experimental and numericalmethods and standards for practical application in an industry environment. For this purpose the target
cases shown in Figure 1, a 𝐿𝑠 = 130𝑚 twin-screw mega yacht with fixed pitch propellers, a 𝐿𝑠 =145𝑚 single-screw container ship with controllable pitch propellers and a 𝐿𝑠 = 24𝑚 fast twin-screw
catamaran for servicing wind farms, are investigated. The consortium consisting of the research
partners SINTEF-Ocean and CNR-INM, the academic partner Technical University Hamburg andthree industry partners Lürssen, Schottel and Helseth with their respective target cases. The first vessel(a) is invoked as a reference target case and thus studied in experimental measurements in full scale
and two different model scale configurations, with a half-model considering the ships centerline
symmetry plane and a full-model with two propellers respectively. Numerically two contrary
approaches for evaluating the flow field are followed, with finite volume methods, both Reynolds
averaged (RANS) and high-fidelity turbulence resolving (DES, LES) are utilized, and a boundary
element method, specifically a panel method. This allows for both highly iterative propeller designtasks requiring fast calculations and detailed investigations of noise generation mechanisms withhigher numerical resource requirements. The multitude of investigations yield the possibility toascertain testing facility influence, repeatability of experimental and numerical investigation withdifferent arrangements, practical applicability of scaling methods, and accuracy of numerical methods
for different geometrical scales and turbulence modelling approaches. Several operation conditions
are analyzed for openwater, with straight and oblique inflow, and behind hull configuration, in wetted
and cavitating conditions.

(a) Mega yacht
Lürssen(b) Container ship
Schottel(c) Wind farm service catamaran
HelsethFigure 1 – ProNoVi Target Cases

2. METHODS
2.1 Experimental
Three different experimental configurations are considered, where the main difficulties lie in theinherent dependence of underwater noise on geometrical characteristics of each. As a result, it iscommon practice to apply a number of corrections to any noise measurements.
2.1.1 Model Scale
The measurements at SINTEF Ocean with a port side half hull model are performed in the Large
Cavitation Tunnel featuring a test section size of 6.0𝑚 ⋅ 1.3𝑚 ⋅ 1.2𝑚 described by a model center
plane and a wooden top plate near the waterline. LDV equipment is mounted on the side window at
the propeller plane, the pressure pick-ups have a sampling frequency of 9.6kHz with a filter cut-off
frequency of 2.0𝑘𝐻𝑧. A Broeel & Kjaer model 8103 hydrophone is located inside a hydrof oil in thetest section and records with 96.0𝐻𝑧. There are three cameras (black) and two high speed cameras(green), with a sampling rate of 2kHz to allow for 6° interval resolution, located with a clear view ofthe propeller as shown in Figure 2. A transfer function is obtained by measuring background noiseand gross noise in order to obtain the propeller net acoustic emissions.

Figure 2 – SINTEF test section and experimental setup
CNR-INM measurements are conducted on a full hull model in the Large Cavitation Channel of
CNR-INM2 with dimensions of 10𝑚 ⋅ 3.6𝑚 ⋅ 2.25𝑚 at the test section as shown in Figure 3 with afree water surface. The set up consists of two hydrophones positioned in correspondence of thepropeller plane with H1 located 112𝑐𝑚 beside the propeller axis on the starboard side and H2 located140𝑐𝑚 below the propeller axis in correspondence of the facility midplane . Additionally, ninepressure gauges are located on the hull as indicated in Figure 4. The hydrophones are miniature, highsensitivity transducers by Brüel & Kjær of the model B&K 8103 with a frequency range of 0.1𝐻𝑧 −180𝑘𝐻𝑧 and a sensitivity of −211𝑑𝐵 𝑟𝑒 1𝑉/𝜇𝑃𝑎. Hydrophone signals are conditioned by a Brüel &Kjær “NEXUS” charge amplifier and then acquired by a 20 channel-24 bit DAW PROSIG P8200. The
pressure gauges are dynamic pressure transducers by PCB, i.e. PCB 106B with a frequency range of
0.5𝐻𝑧 − 60𝑘𝐻𝑧 and a sensitivity of 43.5𝑚𝑉/𝑘𝑃𝑎, flush mounted to the hull vault through dedicatedmetallic inserts. Pressure signals are recorded for a time window of Δ𝑇 = 90𝑠 at the sampling
frequency of 𝑓𝑠 = 100𝑘𝐻𝑧. Cavitation observations are performed through a high-speed camera by
Photron (Photron SAx1 model), rotated by 45° along the vertical axis directed at the starboard
propeller from one side through a 45° inclined water prism attached to the facility window. The
illumination is provided by a 1800𝑊 high-intensity HMI lamp by ARRI and a 1000𝑊 halogen lampby DEDOLIGHT. For the experimental results, transfer functions are calculated with backgroundnoise measurements, which are applied to the propeller measurements, in order to obtain propeller net
noise.

Figure 3 – CNR-INM test section and experimental setup
2.1.2 Full Scale
Full scale measurements of the reference target case mega yacht are done from a work boat, whichis free floating with all engines stopped and power supply from batteries only. The distance to thetrack of the yacht passing by is 113𝑚 in the first passage and 270𝑚 in the second passage. Noise
measurements are conducted with a freely suspended hydrophone. The calibration of the measurement
chain is conducted on scene by a pistonphone with a frequency of 250𝐻𝑧 . The depth of thehydrophone is determined by measurements of the static pressure at the hydrophone and is calculated
2

www.inm.cnr.it/labs/circulating-water-channel/

from the cable angle at water surface, cable geometry, ballast and cable length , leading to a correcteddistance between noise source and observer. Data acquisition is done with a National Instruments
suite, the signal analysis done in Matlab. A pressure sensor type Cera Diver from Van Essen
Instruments is used. GPS position of the hydrophone is recorded with a Garmin GPS and ship positionis tracked from the AIS signal. A Leica range master is used for additional optical control of the
distance from the yacht at closest point of approach.
The measured received levels of underwater radiated noise are converted to monopole source levels
accounting for the Lloyd’s Mirror effect using the following information:• Water depth from echo sounder of the yacht• Source depth from technical data of the propeller and ship general arrangement• Hydrophone depth calculated from submerged cable length and cable angle at the water
surface• Distance ship-hydrophone calculated from GPS-data of the target ship and from mobile
GPS receiver at the hydrophone cable attachment point• Nature of the soil from a geological map
2.2 Numerical
The general challenges associated with the numerical investigations are : the resolution of thepropeller cavitation in particular for the trailing vortices, oblique and thus temporally and spatiallyunsteady inflow, and respecting the vessel wakefield as well as the rudder. While finite volume
methods aspire to resolve turbulence and trailing vortices in exchange for larger numerical resources,
the boundary element method is required as a feasible way for implementation into recurring industry
workflows.
2.2.1 Finite Volume Method
In ProNoVi, two software solutions for the finite volume methods are used, HELYX-core, an
OpenFOAM distribution, with the solver interPhaseChangeDyMFoam and StarCCM+. As a propeller
rotating with respect to a fixed ship hull is an intrinsically transient phenomenon , a full propeller
model and an unsteady PIMPLE simulation scheme is utilized for the finite volume approaches, inboth openwater and behind hull conditions. The propeller rotation is realized with a sliding meshinterface in the form of a cylinder with its rotational axis along the propeller shaftline with one baselocated upstream between propeller and shaft brackets and the other downstream between the propeller
hub cap and the rudder location.
Turbulence modelling is differentiated between isotropic RANS modelling, which employs twoequation models with either a fully turbulent k--SST or a 𝛾 − 𝑅𝑒𝜃 transition approach. For the highfidelity simulations, the turbulence is resolved with LES, either implicit or with Smagorinsky
subgridscale modelling for OpenFOAM. As a hybrid approach the improved delayed DES is appliedwith a delay factor for enhancing the differentiation between RANS and LES on highly refined meshes
and based on an improved formulation with subgrid length scales depending on wall distance, which
is applied for the StarCCM+ approach.
Regarding the physical transport properties an incompressible, isothermal two-phase homogeneous
Eulerian mixture model for water and vapor with volume of fluid phase-fraction capturing is utilized
as a volume-of-fluid method (VOF), where the mass and momentum transport equations of the fluid
mixture are solved. One additional scalar transport equation for the water volume phase fraction 𝛼 toscale the physical properties is required with a source term for cavitation on the right-hand side
𝜕𝛼
𝜕𝑡

𝑚̇

+ ∇ ⋅ (𝛼𝑢⃗ ) + ∇ ⋅ [𝛼(1 − 𝛼)𝑢𝑐 ] = 𝜌 ,𝑙(1)where 𝑢𝑐 is an artificial velocity field to compress the interface. Phase transition is modelled with
the Schnerr-Sauer cavitation model (9), based on a simplified Rayleigh-Plesset equation
𝑑2 𝑅

3 𝑑𝑅 2𝑅 𝑑𝑡 2 + 2 ( 𝑑𝑡 ) =𝑝(𝑅)−𝑝∞
𝜌𝑙

2𝜎

4𝜇
𝑑𝑅
𝜌 𝑅

− 𝜌 𝑅 − 𝑙𝑑𝑡 .

(2)

𝑙In the respective implementations, the vaporization and condensation coefficients 𝐶𝑣 and 𝐶𝑐 are set
to unity, the bubble radius is 𝑅, the nucleation volume fraction 𝛼𝑁𝑢𝑐 , and the nuclei density 𝑛0 = 1 ⋅1012 𝑚−3 and initial nuclei diameter 𝑑𝑁𝑢𝑐 = 1 ⋅ 10−4 (OpenFOAM) and 𝑑𝑁𝑢𝑐 = 1 ⋅ 10−6
(StarCCM+) respectively. Both OpenFOAM and StarCCM+ with their implicit LES and IDDES are
proven to be able to resolve trailing vortices with sufficient mesh refinement in regions of highvorticity. (7,8)
2.2.2 Panel Method
The panel method panMARE is a boundary element spatial discretization for potential flow basedon the work published by Katz and Plotkin (10). It is based on the conservation equation of two
potentials in the fluid volume. After some transformations, a Neumann form of the equation is reachedcontaining the inflow velocities 𝑣𝑀 and external potentials due to waves etc. The function 𝛷𝑒𝑥𝑡 as
well as the surface properties called doublet strength μ and source strength σ, which are used to
substitute the potential on the surface and its derivative in normal direction respectively
1

𝜕 1

1

0=⏟
⃗ + 𝛻𝛷𝑒𝑥𝑡 ∙ 𝑛⃗.
∫ [𝛻𝜇 𝜕𝑛 𝑟 ∙ 𝑛⃗ − 𝛻𝜎 𝑟 ∙ 𝑛⃗] d𝑆 − 𝛻𝛷
⏟
𝑀 ∙𝑛
4𝜋 𝑆
𝐵

(3)

=𝑣⃗𝑀

𝛻𝛷𝑖𝑛𝑑

After solving the resulting equation system, the total velocity 𝑣 ∗ at every location in the simulation
domain can be determined𝑣 ∗ = 𝛻(𝛷𝑖𝑛𝑑 + 𝛷𝑒𝑥𝑡 + Φ𝑀 ),(4)
as well as the corresponding pressure1

𝜕(𝛷𝑖𝑛𝑑 +𝛷𝑒𝑥𝑡 )2

𝜕𝑡𝑝 = 𝜌 𝑔 ∙ (𝑃⃗∞ − 𝑃⃗) − ⏟(𝛻𝛷𝑖𝑛𝑑 − 𝛻𝛷𝑀 + 𝛻𝛷𝑒𝑥𝑡 )2 −1+ ⏟(𝛻𝛷𝑀 )2 + 𝑝∞ ,
2

1 2
= 𝑣
⃗
2 𝑙𝑜𝑐𝑎𝑙

(5)

1 2
= 𝑣
⃗
2 𝑀

[
]
at its location 𝑃⃗. The partially nonlinear model implemented in panMARE for sheet cavitation isbased on Fine (11). On panels identified as cavitating, the doublet strengths are determined byrearranging the Bernoulli equation and integrating the main velocity component to fulfil the dynamic
boundary condition. This is done in a predictor-corrector approach multiple times in one time step.
The cavity thickness is calculated by solving an explicit equation system implementing the kinematicboundary condition, which requires the cavity surface to be a material surface in the flow.
2.2.3 Acoustic Analogy
To consider acoustic effects the integral permeable surface Ffowcs Williams-Hawkings method(12) in the Farassat 1A formulation, based on a generalized Lighthill acoustic analogy, which respects
solid boundary and uniform convection effects, is applied to the flow simulation results for the farfield observer. This method is derived from the compressible Navier-Stokes equations underassumption of a non-viscous medium and reduces the acoustic pressure sources to a non-deformablecontrol surface around the relevant flow structures𝑝 ′ (𝑥, 𝑡 ∗ ) = 𝑝 ′𝑇 (𝑥, 𝑡 ∗ ) + 𝑝𝐿′ (𝑥, 𝑡 ∗ ) + 𝑝𝑄′ (𝑥, 𝑡 ∗ ) ,(6)′which are distinguished by type as pseudo-thickness 𝑝 𝑇
𝑝 ′𝑇 (𝑥, 𝑡 ∗ ) =1 𝜕
𝜌 𝑢 +(𝜌−𝜌0 )(𝑢𝑛 −𝑣𝑛 )] 𝑑𝑆,∫ [ 0 𝑛 𝑟|1−𝑀
4𝜋 𝜕𝑡 𝑆
𝑟|
𝑟𝑒𝑡

(7)

and -loading 𝑝𝐿′
𝑃 ′ +𝜌𝑢 (𝑢 −𝑣𝑛 )

1 1 𝜕

𝑟 𝑛
𝑝𝐿′ (𝑥, 𝑡 ∗ ) = 4𝜋 𝑐 𝜕𝑡 ∫𝑆 [ 𝑛𝑟 𝑟|1−𝑀|
𝑟𝑃 ′ +𝜌𝑢 (𝑢 −𝑣 )

1

]
𝑟𝑒𝑡

𝑟 𝑛
𝑛
𝑑𝑆 + 4𝜋 ∫𝑆 [ 𝑛𝑟 𝑟2 |1−𝑀
]
|
𝑟

𝑑𝑆,

(8)

𝑟𝑒𝑡

whose terminology is originating in rotational noise, as well as quadrupole sources 𝑝𝑄′
1 1 𝜕2𝑇𝑟𝑟𝑝𝑄′ (𝑥, 𝑡 ∗ ) = 4𝜋 𝑐 2 𝜕𝑡 2 ∫𝑉 [𝑟|1−𝑀
]
|
𝑟

𝑟𝑒𝑡

1 1 𝜕

3𝑇 −𝑇

𝑟𝑟
𝑖𝑖
𝑑𝑉 + 4𝜋 𝑐 𝜕𝑡 ∫𝑉 [𝑟2 |1−𝑀
]
|
𝑟

3𝑇 −𝑇

𝑟𝑒𝑡

𝑟𝑟
𝑖𝑖
𝑑𝑉 + ∫𝑉 [𝑟3 |1−𝑀
]
|
𝑟

𝑟𝑒𝑡

𝑑𝑉,

(9)

with the Lighthill stress tensor T. For the reconstruction of the acoustic signal, the individual
contributions are evaluated at the retarded time 𝑡 ∗ = 𝑡 − 𝑟/𝑐, which is the reason that predetermined
observers are selected for the evaluation step. The various approaches in this investigation apply
different simplifications, such as respecting a stationary control surface or neglecting the quadrupole
contributions of Eq. (9). While in HELYX and panMARE, the evaluation is executed at runtime andonly observer signals are reported, the complete control surface is stored for all timesteps in the
StarCCM+ implementation so the acoustic observers may be selected as part of the post-processing.
For the analysis, the control surface is cylindrical around the propeller with the main axis colinear
to the rotation axis or a rectangular box around the propeller and rudder. In the finite volume methods,
an additional difficulty is presented in the restrictions by the sliding mesh interface, as the control
surface requires a stationary underlying mesh and thus is located between the sliding interface and thesurrounding appendages. While the quadrupole sources outside the control surface are neglected for
all approaches, StarCCM+ also calculates the quadrupole sources inside the control volume definedby the surface.
2.3 Acoustic Post-Processing and Comparison
A standard FFT algorithm is applied to the time series data, followed by a conversion to a single
sided spectrum and respective correction factors for energy preservation and windowing. Model scalepressure signals are scaled to full scale for improved comparability with𝑛 𝐷

2 𝜌 𝑟 𝐷𝑃𝑠 = 𝑃𝑚 [(𝑛 𝑠 𝐷𝑠 ) 𝜌 𝑠 𝑟𝑚𝐷 𝑠 ],
𝑚 𝑚

(10)

𝑚 𝑠 𝑚

where the subscript 𝑠 indicates full scale and 𝑚 model scale values. Similarly, frequencies are scaledwith 𝐹𝑠 = 𝐹𝑚 𝑛𝑆 /𝑛𝑚. For the 1/3 octave band representations a domain band pass filter is applied on
the experimental results, while the data obtained from numerical results is synthesized from discrete
narrowband data in frequency domain.
The comparison of hull pressure pulses at propeller blade harmonics evaluates the closest distancediscrete frequency point in the set. For spectral far-field comparison the observer signals in 𝑑𝐵 𝑟𝑒 1 ⋅10−6 𝑃𝑎 are converted to normalized source level signals with
𝑅𝑁𝐿 = 𝑆𝑃𝐿 + 20 log10 (𝑟𝑚 /𝑟𝑠 )(11)
at 𝑟𝑠 = 1𝑚.

3. TEST CASE
Two main operation points for the comparison of the different methods are selected. Coordinate
systems are cartesian with their origin at the intersection of the propeller plane and the rotational axis,
with the positive x-axis directed upstream and the positive z-axis against the gravitation force.
3.1 Propellers and operation points
Two different test cases are considered in Table 2, with one being the public domain propeller
P1595 for the openwater test and the second the confidential P3193 propeller geometry in behind hullcondition with a scaling factor of 𝜆 = 21.078. The coordinate origin for each is at the intersection of
the propeller shaft axis and the propeller plane, which is the center of the cavitation tunnel and thenumerical domains for the openwater cases. In both cases the inflow speed and thus the advance ratio
𝐽 are not measured and the propeller thrust is the defining setting parameter.
To evaluate the consistency of the used methods, first the P1595 propeller geometry in model scalewith a shaft angle of 𝜑 = 0° is compared in open water condition. The location of the hydrophone
𝑥 = ( 0.035, 0.4, 0.128 ) in the experimental investigations, is considered far-field, for a wavelengthof 3𝜆𝑓 , leading to a frequency above 𝑓 > 7.1𝐻𝑧. The operation point is at 𝑘 𝑇 = 0.302 with 𝐽 = 0.60
for a rotation rate of 𝑛 = 30𝐻𝑧 and a cavitation number of 𝜎𝑛 = 2.00 , which features a welldeveloped cavitating tip and hub vortex, as well as significant amount of sheet cavitation on thesuction side starting at the leading edge. While the experiments each have different cavitation tunnel
geometries, the OpenFOAM setup considers the SINTEF cavitation tunnel walls, and StarCCM+ andpanMARE employ a quasi-infinite domain without walls.
To ensure comparability to the full scale measurements, the second comparison focuses on theP3193 propeller geometry given in Table 2 in combination with the reference target case hull with ashaft inclination of 2.75°. For the full scale measurement and the respective numerical comparisons,the operation point is 𝐽 ≈ 0.82 and 𝜎𝑛 = 1.38, designated C1 with the hydrophone position at 𝑥 =( 0, 150, 0 ) given by the full scale experimental setup. The considered model scale operation point
C2 is 𝑘 𝑇 = 0.267 and 𝜎𝑛 = 1.2, leading to an inflow speed corresponding to around 𝐽 = 0.6 − 0.7.
The hydrophone location in the model experiments is 𝑥 = ( 0.095, 0.037, −0.36 ) , which can beconsidered far-field for frequencies 𝑓 > 8𝐻𝑧.
Table 2 – Propeller main parameters
Table 3 – Setups with hull
Parameter

Unit

P1595

P3193

Type
FVM

Diameter

[𝑚]

0.204

0.204

Pitch ratio

[−]

1.188

1.061

Area ratio

[−]

0.626

0.849

Boundary Conditions
Velocity inlet / pressure
outlet / walls

Mesh~25 ⋅ 106 cells~1.2 ⋅ 106 faces propeller

Skew

[°]

42

42

Number of

[−]

4

5

bladesPanelmethodMeasured𝑘𝑇

Axial projection vessel
4200 panels propeller
wakefield / constant
19200 panels propeller
dipole and source strength
wake
Experiment operation
Fixed
Control variable𝑛; 𝑝 / 𝜎𝑛𝑉𝑆 / 𝐽𝑆

3.2 Hull
The reference target case vessel, the Lürssen mega yacht in combination with the P3193 propeller,
represents the main test case. The vessel features counter rotating propellers with a rotation directionof inwards over the top. In the model scale experimental campaigns, the length of the reference target
case vessel is reduced at the middle frames to fit geometrically into the cavitation tunnel, which is
expected to have negligible influence on the wakefield and thus both performance and acoustics. In
both experiments and numerical investigations, the appendages, which are shaft brackets, a twisted
rudder, as well as a diverging propeller hub cap are included in the model as shown in Figure 4 (a).
In the SINTEF cavitation tunnel and the numerical investigations in model scale (Table 3), a halfmodel is used, while the CNR-INM cavitation tunnel and the full scale experimental investigations
consider a full-model, which leads to an additional difficulty in comparing the results between
facilities, as a correction for the second propeller is required. Due to the highly different approaches
followed within ProNoVi, an overview of the different methods used for the model scale investigationsat C2 is provided in Table 4. All numerical calculations in model scale aim to copy the experimental
measurements from the SINTEF cavitation tunnel. For full scale numerical investigations, a freesurface and a quasi-infinite domain parallel to the water surface and a water depth of around 40𝑚 areconsidered. Some additional analyses are undertaken with the other target case hulls and respective
propellers described within the respective section.
Table 4 – Overview of methods for C2
Participant

MethodGeometry

Acoustics

Lürssen
SINTEF

Full scale exp.
Model scale exp.

Real vessel
Cavitation tunnel, Half-model

Simulation of transmission losses
Transfer function

CNR-INM

Model scale exp.

Cavitation tunnel, Full-modelTransfer function

SINTEF

FVM - StarCCM+

Quasi-infinite, Half-model (sym.)

Permeable surface FWH

Schottel

FVM- HELYX
(DES,
LES)
Panel
method(RANS,LES)-

Cavitation tunnel, Half-model

Permeable surface FWH

Infinite, Wakefield

Permeable surface FWH

TUHH

panMARE

Besides the far-field observers, which are hydrophones located in the cavitation tunnels or heldfrom a pilot boat respectively, there are nine pressure sensors on the hull above the propeller as
indicated in Figure 4 (b) for all setups, except the full scale experiment. For the OpenFOAM setup,
additionally the complete shown rectangular surface in (c) on the hull domain boundary is evaluatedvisually to provide a more intuitive way to assess propeller performance with respect to introduced
hull pressure pulses.

(a) Experimental model(b) pressure pick-ups(c) Evaluation boundary surface

Figure 4 – Hull observers locations

4. RESULTS
4.1 Cavitation Pattern
The cavitation pattern on the suction side for C2 (behind hull) reported in the model tests and inthe OpenFOAM and StarCCM+ setups are illustrated in Figure 5. A common occurrence is the leadingedge sheet cavitation starting at mid to outer radii sections and the increased cavitation volume at the
6 o’clock position. However, there is a disparity in reach of the sheet cavity with respect to the lower
radii between the model test setups with one and two propellers. Another mentionable difference
between both numerical approaches is the extent of cavity volume at the upwards rotating outer blade ,which might be an effect of the different wakefield prediction between the setups. Other differences
are the occurrence of a small hub vortex for the StarCCM+ setup, which interacts with the rudder bulbof the twisted rudder and a thin tip vortex filament for the SINTEF experiment for a geometricallength of half a rotation downstream of the propeller plane. The differences might have a large effecton predicted sound, even though the general occurrence of cavitation is identical between the methods.

(a) Exp. SINTEF(b) Exp. CNR-INM(c) OpenFOAM LES(d) StarCCM+ DES

Figure 5 – Cavitation pattern with different methods, C2
4.2 Propeller Openwater Noise
For the different methods at the hydrophone location, a spectral representation of the radiated noiselevel scaled to 1𝑚 for the openwater case with the P1595 scaled to full scale is shown in Figure 6. In(a) the 1/3 octave bands from OpenFOAM, StarCCM+ and panMARE are compared to theexperimental results, which yields some agreement between 25 − 300𝐻𝑧. Only the OpenFOAM setup
predicts SPL higher frequencies in a similar range than the model tests, while panMARE is technicallynot able to predict very high frequencies, StarCCM+ is generally underpredicting the noise, whichmight be a result of the quasi-infinite domain applied in this approach instead of a cavitation tunnel.
In (b) the acoustic evaluation methods of direct pressure calculation within the domain and the FWH
acoustic analogy are compared for OpenFOAM and panMARE, which generally appear to yield
similar results, which is expected and is considered a validation of th is acoustic method. However,some unfavorable differences appear at the lower frequencies, especially the first two harmonics,
which confirm that further research is required, since especially placement effects of the FWH control
surface are not investigated in detail for this case. It is worth mentioning, that while the underlying
data for both (a) and (b) is identical for the OpenFOAM case, the exact dominant frequency
information causing the increased SPL, which might be important for the vessel operation, is lost in
the 1/3 octave representation.

(a) 1/3 octave band results for methods with FWH(b) CFD domain pressure probes vs. permeable surface FWH observer

Figure 6 – Openwater P1595, Hydrophone location
4.3 Behind Hull Noise
For the analysis of the acoustic emissions with hull, initially the incompressible hull pressure atthe pressure pick-ups on the hull at the first four propeller blade passing frequencies are summarized
in Figure 7 for three locations P3, P4 and P10. At C2, wetted and cavitating condition are compared
between the model scale setups for numerical and experimental methods with the amplitudes scaled

to full scale. Although the observer P3 is located directly above the propeller, other observers feature
higher amplitudes, depending on the method. Another peculiarity is the reduced values in cavitating
condition, which might be explained by the steady vapor volumes attenuati ng the acoustic emission
and the low amount of trailing vortex cavitation at this operation point. In general , it is not possible
to determine a clear trend, spatially between observer locations, methodically between approaches, oreven between physics (wetted and cavitating). However, all approaches have in common that thehigher blade harmonics are lower than the first, yet mostly underpredicted by numerical methods,
except for OpenFOAM in cavitating condition, which might be a result of the LES turbulencemodelling, although it has to be noted that the first harmonic is greatly overpredicted.

Figure 7 – Pressure fluctuations at propeller blade harmonics at selected hull observers, C2
In Figure 8, for the far-field, at the hydrophone location, the spectral radiated noise level is given
in narrowband and 1/3 octave band representation for the model scale SINTEF cavitation tunnel
obtained from OpenFOAM, StarCCM+ and the experiment. A good agreement between the octave
bands is achieved between all methods over a wide frequency range from 60 − 2 ⋅ 103 𝐻𝑧, even though
the difference in narrowband is large due to the highly dissimilar sampling rates. In the low
frequencies a clear resolution of the blade harmonics is only accomplished by OpenFOAM. At higher
frequencies, an increase of acoustic pressure appears for StarCCM+, which might be explained bynumerical issues. Similar to the openwater case, a clear allocation of the single sound contributions
is only possible in narrowband representation.

Figure 8 – Behind hull narrowband vs. 1/3 octave band, Hydrophone location, C2
4.4 Scaling Methods
For C1, the scaled results from the model scale experiments are compared to the full scalemeasurement in 1/3 octave bands in Figure 9 (a), where a correction is added to the SINTEF resultsin order to consider the full-model and the second working propeller. As a reference, the DNVEnvironment Transit limit curve (13) is given for which the vessel’s measured signal is below for all
approaches. Data points with background noise of not less than 3𝑑𝐵 compared to the measured noise
are omitted in the model test data. Due to cable vibrations the full scale results are disregarded below
100𝐻𝑧 . In line with previous observations, single contributors are not discernible in thisrepresentation, while (b) shows the narrowband results for two full scale numerical approaches, where
single contributions such as the harmonics or, in the case of the measurement, machinery are distinctly
apparent. As a result of the lower level of detail of the panel method and the high timestep, thepanMARE results feature no high frequency or background noise. Here the vessel geometry is only
considered as a wakefield, which might be an advantage to single out the propeller contributions dueto the fundamental separation of propeller and vessel influence, such as in an optimization workflow.

The source of the high frequency noise around 1600𝐻𝑧 for the OpenFOAM approach is not clear andmight be a numerical issue.

(a) EFD, model test facilities scaled to full scale, 1/3 octave band
representation(b) CFD with full scale setup and sea trial measurements

Figure 9 –Scaling methods, C1
4.5

Advanced Evaluation Methods

P3193

P1595

P3193

LES+Cav

RANS+Cav

RANS

P1595

Figure 10 –Evaluation on simulation boundary patch, C1
For the OpenFOAM model scale simulations at C2, the boundary patch pressure pulse results forthe first two propeller blade harmonics are visualized in Figure 10. The case is calculated with bothpropellers and thus have different frequencies for the harmonics. Compared to the representation as abar graph in Figure 7, there is now a clear spatial pattern discernible and a trend between methods andin this case consideration of the level of physical details of the methods is identifiable. It is apparent
and expected that there is a sound level change between wetted (RANS) and cavitating flow
(RANS+Cav). While the first harmonic experiences no significant change between Reynolds averaging (RANS+Cav) and resolving turbulent length scales (LES), the second harmonic is sever ely
affected, which illustrates the necessity for adequate turbulence resolution at higher frequencies. It is
expected that turbulence and turbulence-cavitation interaction, especially in the propeller slipstream
is the source of noise at higher frequencies. In addition and for industrial applications most importantly,
the characteristics of the propellers with respect to the sound input into the vessel hull are easily andclearly distinguishable.

4.6 Comparison of Vessel Signatures
All ProNoVi target case signatures at their respective design operation points are compared in
Figure 11 in full scale, with the signals from individually placed observers normalized to 1𝑚 forcomparability. The operation points are the above described C1 for the mega yacht (𝑣𝑆 = 21𝑘𝑛, 𝑛 =188𝑟𝑝𝑚) with a power consumption of around 𝑃 ≈ 11.000𝑘𝑊, a vessel speed of 𝑣𝑆 = 18.5𝑘𝑛 for thecontainer vessel with a propeller diameter of 𝐷𝑃 = 5.8𝑚 and speed of 𝑛 = 111𝑟𝑝𝑚 and a power
consumption of around 𝑃 ≈ 7.800𝑘𝑊, and for the wind farm service catamaran a vessel speed of𝑣𝑆 = 19.9𝑘𝑛 with a propeller diameter of 𝐷𝑃 = 0.98𝑚 and speed of 𝑛 = 780𝑟𝑝𝑚 and a power
consumption of 𝑃 ≈ 520𝑘𝑊. The first two are evaluated with the described OpenFOAM setup, thelatter with the StarCCM+ approach. Although there is a significant difference between vessel speeds
and delivered power for the mega yacht and the container vessel the radiated noise levels are similar
over a wide range of frequencies, which may be attributed to the twin-screw setup and noise optimized
propellers for the yacht. The small catamaran on the other hand produces significantly less far-field
noise with its small propellers, despite the high rate of rotation and subsequently similar propeller
blade tip speed. Other possible explanations are due to underlying methods such as use of RANS,
interference with "numerical noise" from the data interpolation on the sliding interface, and omissionof all noise sources between the downstream boundary of propeller region and rudder for the FWH,
which is an important area in the present case due to interaction between propeller slipstream andrudder, and rudder cavitation.

Figure 11 – Comparison of different vessel signatures at their respective operation points

5. DISCUSSION
5.1 Preferred Method
While model tests are considered state of the art for URN, the distinct differences between thefacilities demonstrate some uncertainties. Full scale measurements on the other hand might not be
representative and repeatable, as there is limited control over external test conditions. For highly
iterative propeller design studies, the panel method panMARE delivers adequate underwater noise
results, especially when noise effect trends for the geometrical variation of propeller design
parameters are desired. However, to resolve the propeller slipstream interactions and thus noise
sources, high-fidelity CFD methods, such as FVM with resolution of the larger turbulent length scales
is necessary. The studies prove that LES is preferable, however, the requirements regarding thesimulation time-step and subsequently computational effort may be a feasibility constraint for
widespread industry application at the moment. In addition, a noise signature evaluation requires
several propeller rotations to resolve low frequency events sufficiently and to provide a good dataset
for FFT analysis. Due to improved interpretability, a harmonic evaluation with high spatially resolved
hull patches should be accepted as the new standard, in particular for numerical methods, as a resultof easy implementation. It is clear from the comparison of vessel signatures, that the high-fidelity
numerical methods are capable of obtaining meaningful comparative data between vessel types, which
may be a feasible way to support broader studies by entities pursuing other research directions, suchas analysis of regional or seasonal cumulative noise.
5.2 Open Issues and Directions of Future Research
Depending on the method there are different issues to resolve. For model tests, improved standards
considering the test setup are required to increase accuracy and repeatability. The panel methods

shortcomings at the moment are primarily the lack of volume sources in the propeller slipstream dueto the missing cavitating tip vortex and the interaction with the rudder. For the FVM approach, there
are still several simplifications associated with the Schnerr-Sauer cavitation model, however, it isexpected that ultimately the VOF two-phase treatment might not be sufficient for high frequency noise,
as single bubble implosions are the primary contributors depending on the bubble radius, requiring
Euler-Lagrange coupling. Other shortcomings are the resolution of the cavitating tip vortex, which isthe current bottleneck in setting up simulations and computational effort , meaning that advanced
meshing strategies such as smart and automatic adaptive mesh refinement are the next step in thistechnological evolution.

6. SUMMARY
Different propeller geometries have been investigated regarding underwater radiated noise inopenwater and behind hull condition in model and full scale. The approaches consist of two different
size model scale test facilities with a half- and a full-model, a full scale measurement, a panel method
and two software distributions for FVM. Generally, the results of all methods are in a good agreement
range with respect to each other, confirming all as feasible ways forward, however, shortcomings
regarding the accuracy are found. Notably the comparison of equal setups in experiment and numericalinvestigations, such as the model scale C2 and full scale C1 comparison, illustrate the remaining
difficulties.

ACKNOWLEDGEMENTS
The authors are very grateful for the support and funding by MarTERA, represented by BMWi project (03SX461C) “ProNoVi” for the German partners, the Research Council of Norway for the
Norwegian Partners (Project 284501) and MIUR-project “ProNoVi” for the CNR-INM.

REFERENCES
1. Frisk GV. Noiseonomics: The relationship between ambient noise levels in the sea and global economic
trends. Scientific Reports; 2012.
2. Branstetter BK, Leger JS, Acton D, Stewart J, Houser D, Finneran JJ, et al. Killer whale (Orcinus orca)
behavioral audiograms. The Journal of the Acoustical Society of America. 2017;4.
3. O’Hara J, Wilcox J. Avoidance Responses of Loggerhead Turtles, Caretta caretta, to Low Frequency
Sound. Copeia. 1990;6:564–7.
4. Casper BM, Lobel PS, Yan HY. The hearing sensitivity of the little skate, Raja erinacea: A comparison of
two methods. Environmental Biology of Fishes. 2003;8.
5. IMO. Guidelines for the Reduction of Underwater Noise from Commercial Shipping to Address Adverse
Impacts on Marine Life. 2014.
6. Port of Vancouver Vancouver Fraser Port Authority, editor. ECHO Program 2021 Annual report. 2022.
7. Kimmerl J, Mertes P, Abdel-Maksoud M. Application of Large Eddy Simulation to Predict Underwater
Noise of Marine Propulsors. Part 1 Cavitation Dynamics. Journal of Marine Science and Engineering.
2021;(778).
8. Krasilnikov V. CFD modelling of hydroacoustic performance of marine propellers: Predicting propeller
cavitation. Proceedings of the 22nd Numerical Towing Tank Symposium. 2019;
9. Schnerr GH, Sauer J. Physical and Numerical Modeling of Unsteady Cavitation Dynamics. 4thInternational Conference on Multiphase Flow. 2001;
10. Katz, Plotkin A, Plotkin J. Low-Speed Aerodynamics. 2nd ed. Cambridge, USA: Cambridge University
Press; 2001.
11. Fine NE. Nonlinear Analysis of Cavitating Propellers in Nonuniform Inflow. Cambridge, USA:
Massachussetts Institute of Technology; 1992.
12. Francescantonio P. A New Boundary Integral Formulation For The Prediction Of Sound Radiation.
Journal of Sound and Vibration. 1997;
13. DNV GL AS, editor. DNV-GL Rules for Classification Ships, Part 6 Additional class notations Chapter,
7 Environmental protection and pollution control. 2017.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022 in Gyeongju, Korea

ABS-0410

Characterization of cavitating and non-cavitating flow noise by
pump-jet propeller of submarine
Garam KU1; Junbeom HA1; Cheolung CHEONG1; Hanshin SEOL2; Hongseok JEONG2
1

School of Mechanical Engineering, Pusan National University, 2, Busandaehak-ro 63beon-gil, Geumjeong-gu,
Busan 46241, Republic of Korea
2

Korea Research Institute of Ships and Ocean Engineering, 32, Yuseong-daero 1312beon-gil, Yuseong-gu,
Daejeon 34103, Republic of Korea

ABSTRACTIn this study, the hybrid computational hydro-acoustic approach was applied to characterize the relative
contribution of the rotor, stator, and duct constituting a pump-jet propeller of a submarine to the underwaterradiated noise in both cavitating and non-cavitating flow conditions. The flow field was simulated using the
Reynolds-Averaged Navier-Stokes (RANS) solver combined with the homogeneous mixture model forcavitation. The acoustic field was predicted using the Ffowcs Williams and Hawkings (FW-H) integral
equation. The three types of integral surfaces were used to compare the relative contribution of flow noise
sources in the pump-jet propeller to the far-field radiated noise. The first is the single permeable integral
surface enclosing the entire pump-jet propulsion system. The second consists of the three impermeable
integral surfaces of the rotor, stator, and duct. The third consists of the inflow/outflow planes and the sideouter solid surface of the duct enclosing the entire pump-jet system. The predicted acoustic pressure signals
are compared in terms of the directivity on a virtual spherical surface of radius 1 m with its origin on thepropeller center.
Keywords: Flow noise, Pump-jet propeller, Cavitation, Acoustic analogy

1. INTRODUCTION
Frequent extreme weather events due to climate change threaten human survival. Carbon dioxide(CO2) generated by industrial activities is considered a potential cause. The international maritime
organization (IMO) has proposed regulations to suppress the CO2 generated from the ship [1] and, atthe same time, recommends reducing the underwater noise from propellers to conserve the marine
ecosystem [2-4]. Since liquefied natural gas (LNG) and nuclear power are alternatives to diesel fuel,nuclear power generation is tried as the future engine system in conventional ships and submarines
due to its plentiful energy and carbon-free characteristics [5]. Along with these trends, the pump-jet
propeller, which is known to have a higher efficiency than the conventional propeller but is difficult
to use due to its complex design and heavy weight [6,7], is being developed and applied as a futuresubmarine propulsion system. However, because the noise performance is a crucial parameter for
ensuring the survivability and successful tactics of the submarine, it is essential to characterize thepump-jet propeller noise. Therefore, this study investigates the cavitation and non-cavitation noise of
the pump-jet propeller installed on the DARPA suboff submarine body. The incompressible two-phase
Reynolds-Averaged Navier-Stokes (RANS) equation is applied to describe the flow field around thepropeller and the submarine body. The Schnerr-Sauer cavitation model based on the homogeneous
mixture assumption is used to simulate the cavitation flow field. The acoustic analogy of Ffowcs
Williams and Hawkings (FW-H) integral equation is used to estimate the underwater-radiated noisefrom the propeller. The three integral surfaces are set up to investigate the relative contribution of
pump-jet components, such as stator, duct, and rotor.

1

garamku5671@pusan.ac.kr

2. NUMERICAL METHODS
2.1 Submerged body and simulation domain
The submerged body consists of DARPA suboff submarine body and pump-jet propeller, and thesubmerged body is at the center of the simulation domain. The simulation domain size is 2.8 m x 12.5m x 1.8 m (width x length x height), which is the same as the dimensions of the test section of LCT[8]. The pump-jet propeller has seven rotor blades and 11 stator blades, and tip clearance between therotor and duct is 0.5 mm. The diameter of the rotor is 0.21 m.

2.2 Governing equation and boundary conditions
The incompressible Reynolds-Averaged Navier-Stokes (RANS) equation based on thehomogeneous mixture assumption is applied to describe the cavitation and non -cavitation flow fieldof the pump-jet propeller and the submarine body. The RANS equations combined with thehomogeneous mixture model are written in the form,𝜕𝜌𝑚+ ∇(𝜌𝑚 𝑣⃗𝑚 ) = 0
𝜕𝑡
𝜕
𝑇 )]
(𝜌 𝑣⃗ ) + ∇ ∙ (𝜌𝑚 𝑣⃗𝑚 𝑣⃗𝑚 ) = −∇𝑝 + ∇ ∙ [𝜇𝑚 (∇𝑣⃗𝑚 + ∇𝑣⃗𝑚
+ 𝜌𝑚 𝑔⃗
𝜕𝑡 𝑚 𝑚(1)

𝛼𝑙 + 𝛼𝑣 = 1, 𝛼𝑙 𝜌𝑙 + 𝛼𝑣 𝜌𝑣 = 𝜌𝑚 , 𝛼𝑙 𝜇𝑙 + 𝛼𝑣 𝜇𝑣 = 𝜇𝑚
𝜕𝜌𝑚
+ ∇(𝜌𝑚 𝑣⃗𝑚 ) = 0𝜕𝑡(2)Here, 𝜌 , 𝑣 , 𝑝 , 𝜇 , 𝑔, and 𝛼 denote density, velocity, pressure, viscosity, gravitational
acceleration, and volume fraction. The subscripts of ‘m’, ‘ l’, and ‘v’, and the superscript ‘ ⃗⃗⃗⃗’ mean
the mixture, liquid, vapor properties, and vector components, respectively.
To describe the phase transfer between liquid and vapor, Schnerr and Sauer cavitation model isused. The k-ω SST turbulence model is applied as a closure model. The above-described equations
are numerically solved using the ANSYS Fluent.
The inflow and outflow boundary conditions are set by the velocity inlet of 3.15 m/s and pressure
outlet, respectively. The applied pressure values at the outlet are 101 kPa for non-cavitation and 15
kPa for cavitation conditions. The rotating speed of the pump-jet propeller is 11.213 rps, and thesliding mesh technique is applied to describe the rotating motion. The geometry and boundary
conditions are presented in Figure 1.

Figure 1 – Submarine and pump-jet propeller geometries and boundary conditions in simulation domain
Based on the simulated results, the radiated noise is predicted using the Ffowcs Williams and Hawkings (FWH) equation [9-11]. The related equations are written in the form,

4𝜋𝑝′ (𝑥, 𝑡) =𝜕
𝑄(𝑦, 𝜏)𝜕𝐹𝑖 (𝑦, 𝜏)] 𝑑𝑆(𝑦) −] 𝑑𝑆(𝑦)∫ [∫ [𝜕𝑡 𝑆 𝑟|1 − 𝑀𝑟 |𝜕𝑥𝑖 𝑆 𝑟|1 − 𝑀𝑟 |(3)

𝑇𝑖𝑗 (𝑦, 𝜏)𝜕2+] 𝑑𝑉(𝑦)∫ [𝜕𝑥𝑖 𝜕𝑥𝑗 𝑉 𝑟|1 − 𝑀𝑟 |Here, a superscript ‘′’ and subscript ‘r’ mean the fluctuation property and radiated directional
component, respectively, and 𝑟 = |𝑥 − 𝑦|. S and V denote the surface and volume. On the right-handside of Eq.(3), each term denotes the monopole, dipole, and quadrupole noise sources, respectively.

2.3 Grid system in simulation domain
The grid system is separated into three parts. Region 1 is the rotating grids, including the rotor
blades, Region 2 is the meshes containing the propulsion system except for the rotor, and Region 3 isthe other grids enclosing the entire submarine body. The applied grid type is the poly-hexa type, andthe grid system is generated using the Fluent Meshing tool. The number of grids for Regions 1, 2, and3 are 2.3 M, 5.5 M, and 5.5 M, respectively. Seven prism layers are set to describe the boundary layer
flow. The grid system is presented in Figure 2. The y+ distribution on the submerged bodies is set to
below five as shown in Figure 3.

Figure 3 – y+ distribution

Figure 2 – Entire grid system in simulation domain

Three types of integral surfaces for noise sources are selected, as shown in Figure 4, to predict theunderwater-radiated noise from the propulsion system.

(a) All(b) Type 1(c) Type 2(d) Type 3

Figure 4 – Integral surfaces; (a) all surfaces; (b) permeable surface; (c) impermeable surface; (d)combination of permeable and impermeable surfaces
The integral surfaces used in this study can be classified into three types: one is a permeable type,the second one is an impermeable type, and the third one is a combination of permeable andimpermeable types. Figure 4(b) shows the permeable surface enclosing the entire propulsion system.
The impermeable surface shown in Fig. 4(c) consists of solid surfaces of the rotor, stator, and duct.
The integral surface consists of permeable inflow and outflow surfaces denoted by red-coloredsurfaces and the outer solid surface of the duct, as shown in Fig. 4(d).

3. NUMERICAL RESULTS
Figure 5(a) shows the pressure distribution on the cross-sectional planes of the pump-jet propulsion
system. The higher pressure region can be identified in the upper part of the cross-sectional plane 1,
which seems to be affected by the wakefield formed by the submarine hull. The flow patterns
associated with the stator and rotor blades can be identified in the other cross-sectional planes from 2
to 10. Figures 5(b) and (c) show the pressure distributions on the suction side for non-cavitation andcavitation conditions, respectively. It can be seen in Fig. 5(c) that cavitating flow occurs on the small
area of the blade tip.

(a)(b) non-cavitation condition(c) cavitation condition

Figure 5 – Simulation results: (a) gauge pressure distribution at sliced planes; pressure distributions on
suction side for (b) non-cavitation condition; (c) cavitation condition with iso-surface of 𝛼𝑣 = 0.5
Based on the flow simulation results, the acoustic pressure generated by the pump-jet was predictedby applying the FW-H formula on each of the three types of integral surfaces. The predicted results
are compared in terms of directivity which is computed at 1 m away from the center of the pump-jet
propeller on the xy-plane. The predicted directivities are compared in Figure 6.

(a) Type 1(b) Type 2(c) Type 3

Figure 6 – Comparison of predicted directivity for integral surfaces of (a) type 1; (b) type 2; (c) type 3

Figure 6(a) compares the non-cavitation and cavitation noise obtained from the integral surface oftype 1. The cavitation noise levels are much higher than the non-cavitation noise ones for all directions,and the cavitation noise directivity reveals the monopolar feature whereas the non-cavitation noise
directivity shows the dipolar characteristics. Figure 6(b) compares the non-cavitation and cavitationnoise levels predicted using the integral surface of type 2. It can be seen that there is no difference
between the two cases because this integral surface includes only the thickness and loading noise
sources and thus cannot consider the cavitation noise source. Notably, the directivity pattern of the
non-cavitation noise is very similar between the two integral surfaces of types 1 and 2. Figure 6(c)shows the directivities for the integral surface of type 3. The cavitation noise levels are much higher
than the non-cavitation ones for all directions, which is similar to the result of Fig. 6(a). In addition,
the cavitation noise levels are the same as those obtained from the monopolar surface source, which
reveals the monopolar characteristics of the cavitation noise. However, the non-cavitation noise levels
are slightly higher than those in the other two integral surfaces. The reason for this difference needs
to be clarified in a future study.

4. CONCLUSIONSIn this study, the pump-jet propulsion noise in the non-cavitation and cavitation conditions wasinvestigated. The DARPA suboff submarine body was also used to consider the effects of upstream
incident flow due to the hull body on the flow and noise of the pump-jet propulsion system. The entire
computational domain was constructed to reproduce the same conditions of the corresponding
experiments which were carried out in the test section of the LCT. The hydrodynamic flow fieldaround the pump-jet and the submarine body was predicted using the incompressible RANS solver
combined with the homogeneous model for cavitation. The FW-H equation was employed to predictthe underwater-radiated acoustic pressure from the pump-jet propulsion system. The three types ofintegral surfaces were utilized to characterize the pump-jet propeller noise. It was found that thecavitation noise levels were much higher than the non-cavitation noise ones. In addition, thedirectivity of the cavitation noise revealed the monopolar characteristics, whereas that of the noncavitation noise showed the dipolar feature. However, the results obtained from the integral surfaceof type 3, which consisted of the permeable and impermeable surfaces, differed slightly from the othertwo results. The reason for the difference needs to be clarified in a future study.

ACKNOWLEDGEMENTS
This study was carried out as a project of ‘Future Submarine Low Noise Propeller ResearchLaboratory’ of KRISO supported by Defense Acquisition Program Administration and Agency for
Defense Development.

REFERENCES
1. International Maritime Organization (IMO) "The Fourth IMO Greenhouse Gas Study 2020" International
Maritime Organization, 4 Albert Embankment, London SE1 7SR (2020)
2. International Maritime Organization (IMO) "Adoption of the code on noise levels on board ships" ANNEX
1, Resolution MSC.337(91) (2012)
3. International Maritime Organization (IMO) "Adoption of amendments to the international convention forthe safety of life at sea, 1974, as amended" ANNEX 2, Resolution MSC.338(91) (2012)
4. International Maritime Organization (IMO) "Guidelines for the reduction of underwater noise fromcommercial shipping to address adverse impacts on marine life" MEPC.1/Circ.883 (2014)
5. K. Jun, Y. Hwan and K. Hyoung "CFD analysis for air cooling stack of hybrid residual heat removal systemusing air and sea water for ship SMR" (in Korean), Proc. Winter Conf. Fluid Machy. (KSFM) (2020)
6. B. Allotta, L. Pugi, F. Bartolini, A. Ridolfi, R. Costanzi, N. Monni and J. Gelli "Preliminary design andfast prototyping of an autonomous underwater vehicle propulsion system" Proc. Inst. Mech. Eng. Part M
J. Eng. Marit. Environ. 229(3) (2015)
7. G. Pan, L. Lu and P. K. Sahoo "Numerical simulation of unsteady cavitating flows of pump-jet propulsor"
Ships and Offshore Struc. 11(1), 64-74 (2016)

8. I. Park, J. Kim, K. Kim, J. Ahn, Y. Park and M. Kim "Numerical analysis of the wake of a surface shipmodel mounted in KRISO large cavitation tunnel" (in Korean) J. Soc. Nav. Archit. Kr. 53(6), 494-502(2016)
9. G. Ku, S. Ryu and C. Cheong "Numerical investigation into cavitation flow noise of hydrofoil using
quadrupole-corrected Ffowcs Williams and Hawkings equation" (in Korean) J. Acoust. Soc. Kr, 37(5)(2018)
10. B. A. Singer, D. P. Lockard and G. M. Lilley "Hybrid acoustic predictions" Comput. Math. with Appl. 46,
647-669 (2003)
11. F Farassat "Derivation of formulations 1 and 1A of Farassat" No. L-19318 (2007)

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022 in Gyeongju, Korea

ABS-0411

Development of innovative monitoring method for underwaterradiated noise from ship propeller using hull surface pressure
signalJunbeom Ha1; Garam Ku2; Cheolung Cheong1; Hanshin Seol3; Hongseok Jeong312School of Mechanical Engineering, Pusan National University, Republic of Korea

Center for Advanced Air-conditioning Refrigeration and Energy, Pusan National University, Republic of Korea
3

Korea Research Institute of Ships and Ocean Engineering, Republic of Korea

ABSTRACTIn this study, an innovative method is developed to monitor the underwater-radiated noise (URN)
from a ship propeller using a local surface pressure signal. The developed method decomposes thesurface pressure signal into the compressible and incompressible pressure components using thewavenumber-frequency transform. The URN is predicted by applying the wall reflection correction
and the propagation loss to the decomposed compressible pressure. The KVLCC2 ship with aprototype propeller is considered. The model-scale experiment is performed in the Large Cavitation
Tunnel (LCT) in the Korea Research Institute of Ship and Ocean Engineering (KRISO). A highaccuracy compressible multiphase Delayed Detached Eddy Simulation (DDES) is performed for thesame submerged body. Acoustic pressure radiated from the propeller is predicted using the Ffowcs
Williams and Hawkings(FW-H) integral formulation, and its validity is confirmed by comparing thepredicted acoustic pressure with the measured. Finally, the URN predicted using the proposedmonitoring method is compared with the FW-H integral equation result. There is excellent agreement
between the two results, which confirms the validity of the proposed monitoring method. From theresult, it is believed that the present process enables real-time monitoring of the URN of a ship byusing surface pressure signals without direct measurement of acoustic pressure radiated from the shipin the far neighboring sea.
Keywords: Underwater-radiated noise, Underwater propeller noise. Wavenumber-frequency transform, Flownoise, Cavitation noise, Compressible pressure

1. INTRODUCTION
Various types of cavitation occurring in an underwater propeller cause acoustic pressure of a highlevel, which is known to lead to the mass extinction of marine life and the occurrence of deformed
fish by disturbing the natural acoustic signal of the marine ecosystem (1,2). As the environmental
pollution problems of the marine ecosystem worsen, the International Maritime Organization (IMO)
tries to regulate underwater-radiated noise to protect the marine ecosystem. Accordingly, a lot of
studies are actively conducted to develop low-noise propulsion systems without sacrificing theirperformance (3).
Some studies were carried out to predict underwater-radiated noise (URN) of a full-scale ship fromthe measured or predicted ones of a scale model. In experimental studies, the URN of full-scale models
was predicted using the correction methods proposed by ITTC and the semi-empirical formula (4-7).
However, it is not successful until now because different and complex noise generation mechanisms
are involved depending on operation conditions. As for the numerical approaches used to overcome
the limitations of the experimental methods, the URN of the scaled and full models were predicted by
performing direct numerical simulations on noise (8, 9). In addition, systematic numerical methods
gjdj152@pusan.ac.kr; ccheong@pusan.ac.kr
garamku5671@pusan.ac.kr
3
seol@kriso.re.kr; hsj@kriso.re.kr
12

were developed for reliable noise prediction. Seol et al. (10, 11) predicted the propeller’s cavitation
flow using the potential-based panel method and predicted the sheet cavitation noise using the FW-H
equation, where the time variation in the cavitation volume is used as a monopole source. Ku et al.
(12, 13) developed Eulerian-Lagrangian coupled simulation technique to predict the tip vortex
cavitation (TVC) flow and noise more accurately for elliptic wings and high-skew propellers.
Although there have been many studies to predict the URN of ships due to underwater propellers
as described above, few studies are carried out on the real-time monitoring techniques of URN, whichenables real-time control of URN during ship operation and thus provides practical measures to copewith noise regulation for the protection of the marine ecosystem. The present study aims to develop areal-time monitoring method of URN due to underwater propellers by using the local surface pressureof a ship which can be easily measured during ship operation. The key algorithm of the proposed
method is based on the extraction of compressible pressure components from the surface pressure
field and the correction due to its wall reflection. In the first phase, the compressible multiphase DDES
is performed to capture flow noise generation and propagation accurately. Then, the URN due tocavitating flow of an underwater propeller is predicted by using the FW-H integral equation. The
validity of hydrodynamic and acoustic simulations is confirmed by comparing the predicted resultswith the measured data. In the second phase, the URN is predicted using the information of the surfacepressure field. The compressible pressure is extracted by applying the wavenumber-frequency
transform to the local surface pressure field on the stern part. The algorithm for decomposing thesurface pressure into the compressible and incompressible pressure components w as verified in thepreceding studies (14, 15). Additional wall reflection effects are considered to predict the URN fromthe decomposed compressible pressure field. Finally, the URN predicted using the surface pressure
field is compared with that using the FW-H, which shows the validity of the present method.

2. Numerical methods
2.1 Target geometries, grids, and boundary conditions
Fig. 1(a) shows the target geometries and computational domain. The scale model of the KVLCC2
hull and a prototype propeller are considered, and the computational domain is the same dimension
as the test section of the LCT in KRISO. As boundary conditions, the inlet flow velocity and outlet
gauge pressure are set 7 m/s and 0 Pa, respectively. The rotational speed of the propeller is 37.05 rps,
and the no-slip condition is set on the side and bottom walls of LCT and the surface of the hull andpropeller.
The grids of poly-hex type are used for entire computational domains. The rotating part containing
the propeller is constructed with more dense grids to simulate the TVC more accurately. In addition,
the flow region around the stern is also resolved with more dense grids to capture hull wake. The
prism grids are constructed to predict boundary layer flow on the wall surface. The dimensionlesswall distance variable, y+, is configured to be about 30 for the LCT and hull and less than 5 for thepropeller. The hydrodynamic simulation is performed by using about 14 million grids. Fig. 1(b)depicts the grid configuration of the entire computational domain with the zoomed views of the target
geometries.

Figure 1 – (a) Target geometries, simulation domain and boundary conditions; (b) grids for simulation.
2.2 Governing equations and numerical schemes
The flow simulation is performed using the homogeneous mixture model. For stable convergenceof two-phase flow simulation, the steady-state RANS simulation is first performed, the unsteady
RANS is secondly performed from the steady RANS result, and the DDES simulation is finally carriedout from the initial condition obtained from the unsteady RANS result. The governing equations of

the homogeneous mixture RANS are written in the form,∂ρm∂(ρ 𝑢̅ ) = 0+∂t∂x𝑖 m 𝑖∂∂∂𝑝̅∂∂∂u̅i ∂u̅𝑗 2 ∂uk(ρmu̅i ) +(ρm u̅i u̅𝑗 ) = ρm g −−(ρm ui′ uj ′ ) +
[μm (
+
− δ
)]
∂t
∂xj
∂x𝑖
∂xi
∂xj
∂xj ∂xi 3 ij ∂xk

(1)
(2)
(3)

αl + αv = 1, ρm = ρv αv + ρl αl , μm = μv αv + μl αl

For the cavitation model, the Schnerr-Sauer model is applied. The k-ω Shear Stress Transport (SST)model is used as a closure model. In the SST-based DDES, the boundary layer near the wall is
calculated using the RANS, and the other region is calculated with the Large Eddy Simulation (LES).
The following shows the transport equation of DDES.
∂ρk ∂ρUi k
∂
𝜕𝑘
∂k
ρ√k 3
(4)
+
=
+ Pk −[(𝜇 + 𝜎𝑘 𝜇𝑡 )] (μ + σk μt )
∂t
∂xi
∂xi
𝜕𝑥𝑖
∂xi
lDDES
∂ρω ∂ρUi ω∂∂ω1 ∂k ∂ωρ(μ + σk μt )+=+ 2(1 − F1 )ρσω2+ α Pk − βρω2
(5)
∂t
∂xi
∂xi
∂xi
ω ∂xi ∂xi
μt
(6)

lDDES = lRANS − fd max(0, lRANS − lLES )fd = 1 − tanh[(Cd1 rd )]𝐶𝑑2 , rd =

νT + ν

.

κ2 d2 √0.5 • (s 2 + ohm2 )(7)

The SIMPLE algorithm is applied to simulate the flow field. The 2 nd -order upwind scheme is used
for spatial derivative, the bounded 2 nd-order scheme is for the momentum equation, the 1st-orderscheme is for the volume fraction, and the 2nd-order upwind scheme is for the turbulent transport
equations. The time step is set to correspond to the rotation of the propeller by 0.1 degrees.
2.3 Compressibility of fluid
Reliable simulation of the compressibility effects of fluid is critical to the successful separation ofincompressible and compressible pressure components. For compressible flow simulation, the energy
and state equations are additionally employed. The energy equation is written as follows,𝜕(8)(𝜌 𝐸) + 𝛻 ∙ [𝑣⃑(𝜌𝑚 𝐸 + 𝑝)] = 𝛻 ∙ (𝑘𝑒𝑓𝑓 𝛻𝑇) + 𝑆𝐸
𝜕𝑡 𝑚
𝑝
𝑣2
𝑤ℎ𝑒𝑟𝑒 𝐸 = ℎ − +𝜌2Here 𝑘𝑒𝑓𝑓 is the effective thermal conductivity, and 𝑆𝐸 means the heat source. For thecompressibility of liquid water, Tait’s equation is used as the state equation of liquid in the form,
ρ 𝑛
Q0 𝑛
K
(9)
( ) =( ) =( )
ρ0
Q
K0
(10)
K = K 0 + n∆P
where Q, ρ, and K denote the volume, density and bulk modulus of liquid. The following is an ideal
gas equation to consider the compressibility of vapor.
pop + p
ρ=
(11)
R
Mw T
Where 𝑅 , 𝑀𝑤 and T is the general gas constant, the molecular weight, and the temperature.
Through the ideal gas equation, it is possible to calculate the density and volume of the vapor.
Compressible flow simulation is performed by considering both water and vapor compressibility
through Eqs (8) to (10).
2.4 Ffowcs Williams and Hawkings
The FW-H equation is used to predict flow noise due to the cavitation flow of the underwater
propeller. The FW-H equation derived from the Navier-Stokes equation has been used in many
preceding studies (16). The FW-H equation is written as follows,
4𝜋𝑝′ (𝑥, 𝑡) =𝑇𝑖𝑗 (𝑦, 𝜏)𝜕𝑄(𝑦, 𝜏)𝜕𝐹𝑖 (𝑦, 𝜏)𝜕2∫ [] 𝑑𝑆(𝑦) −∫ [] 𝑑𝑆(𝑦) +∫ [] 𝑑𝑦
𝜕𝑡 𝑆 𝑟|1 − 𝑀𝑟 |𝜕𝑥𝑖 𝑆 𝑟|1 − 𝑀𝑟 |𝜕𝑥𝑖 𝑥𝑗 𝑉 𝑟|1 − 𝑀𝑟 |(12)𝑄 = [𝜌(𝑢𝑖′ + 𝑈𝑖 ) − 𝜌0 𝑈𝑖 ]𝑛̂𝑖

where𝐹𝑖 = [𝜌𝑢𝑖′ (𝑢𝑗′ + 𝑈𝑗 ) + 𝑝𝛿𝑖𝑗 ]𝑛̂𝑖
𝑇𝑖𝑗 = 𝜌𝑢𝑖′ 𝑢𝑗′ + [(𝑝 − 𝑝𝑜 ) − 𝑐𝑜2 (𝜌 − 𝜌0 )𝛿𝑖𝑗 ]and

𝑈𝑗 = (1 − 𝜌/𝜌𝑜 )𝑣𝑗 + (𝜌𝑢𝑗 )/𝜌𝑜

The right-hand side of the FW-H equation consists of monopole, dipole, and quadrupole noise sources.
However, as the contribution of the quadrupole term is much less than the other terms in low Mach
number flows, it is ignored in this study.
The permeable integration surface, including flow noise sources, is used to predict the URN. The
resultant Farassat's 1A formulation (17) is written in the following form,
𝜌0 𝑈𝑛 (𝑟𝑀̇𝑟 + 𝑐0 (𝑀𝑟 − 𝑀2 ))𝜌0 (𝑈̇𝑛 + 𝑈𝑛 )′ (𝑥,4𝜋𝑝𝑇 𝑡) = ∫ [] 𝑑𝑆 + ∫ [
] 𝑑𝑆
(13)
2
𝑟 2 (1 − 𝑀𝑟 )3
𝑓=0 𝑟(1 − 𝑀𝑟 )
𝑓=0
𝑟𝑒𝑡

1
𝐿̇𝑟
4𝜋𝑝𝐿′ (𝑥, 𝑡) = ∫ []𝑐0 𝑓=0 𝑟(1 − 𝑀𝑟 )2

𝑟𝑒𝑡

𝑟𝑒𝑡

𝐿𝑟 − 𝐿 𝑀
𝑑𝑆 + ∫ [ 2] 𝑑𝑆
3
𝑓=0 𝑟 (1 − 𝑀𝑟 ) 𝑟𝑒𝑡

𝐿𝑟 (𝑟𝑀̇𝑟 + 𝑐0 (𝑀𝑟 − 𝑀2 ))
1
+ ∫ [
]
𝑐0 𝑓=0𝑟 2 (1 − 𝑀𝑟 )3

𝑑𝑆

(14)

𝑟𝑒𝑡
𝜌𝑢

𝜌

𝑗
where 𝑈𝑗 = (1 − ) 𝑣𝑗 + , 𝐿𝑖 = 𝑃𝑖𝑗 𝑛̂𝑗 + 𝜌𝑢𝑖 (𝑢𝑛 − 𝑣𝑛 )𝜌0𝜌0Here, the superscript " ̇ " and "ret" mean the time derivative and the retarded time. The subscript"n" and "r" denote the normal and observer-directional components. The resultant acoustic pressure
can be expressed in the form.

𝑝′ (𝑥, 𝑡) = 𝑝𝑇′ (𝑥, 𝑡) + 𝑝𝐿′ (𝑥, 𝑡)(15)

2.5 Wavenumber-Frequency transform
The pressure perturbation induced on the surface wall by the flow disturbance is a mixture of theincompressible pressure perturbation caused by the turbulent boundary layer and the compressiblepressure perturbation formed by the acoustic wave. In this study, the wavenumber-frequency
transformation is used to separate compressible pressure field from the surface pressure field in thespace-time domain (15,16).
The wavenumber-frequency spectrum in the wavenumber and frequency domains is obtained bytaking the Fourier transform of pressure in the space and time domains . The cross-correlation ofpressure can be expressed in the following form,𝐺(𝜉, 𝜏) = 𝐸[𝑝(𝑥, 𝑡)𝑝(𝑥 + 𝜉, 𝑡 + 𝜏)](16)

where 𝑝, 𝜉, and 𝜏 denote the pressure, distance-vector, and time delay. The Fourier transform fromthe space-time domain to the wavenumber-frequency domain is written in the following form,∞∞∞

𝑆(𝑘𝑥 , 𝑘𝑦 , 𝜔) = ∫ ∫ ∫𝐺(𝝃, 𝜏)𝑒 −𝑗(−𝒌𝝃−+𝜔𝜏) d𝜉1 d𝜉2 𝑑𝜏

(17)−∞ −∞ −∞To separate the compressible component, the following equation can be used:𝑘𝑎 = 𝜔/𝑐0 = √𝑘𝑥21 + 𝑘𝑥22 + 𝑘𝑥1 𝛭(18)

where 𝑈0 is the mean flow velocity, 𝛭 is the Mach number. The spectral components of pressure
satisfying |𝑘| ≤ 𝑘𝑎 at the given frequency can be determined to be the compressible components.

3. Experimental method
A model-scale measurement is conducted in LCT located at KRISO to check the validity of thenumerical simulation. Fig. 2(a) shows the overall schematic of the LCT. The dimension of the test
section is 12.5 m × 2.8 m × 1.8 m. A set of pressure sensors is installed on the hull above thepropeller plane, as shown in Fig. 2(b), and a hydrophone is installed below the test section to measureacoustic pressure due to the propulsion system. Each signal is measured at the sampling rate of
262,144 Hz for 60 sec. The measured time data is transformed to Power Spectrum Density (PSD) byusing the Hanning window with 75% overlap. Also, flow visualization is made to capture the detailed
configuration of cavitation flow on the propeller.

Figure 2– Experimental method; (a) Schematic of the LCT; (b) location of pressure sensors.

4. Numerical Results
4.1 Flow simulation results
Firstly, the steady RANS simulation is performed for bare hull configuration to check the hull
wake-field. Then, the steady RANS simulation with the propeller is performed for fast convergenceof the following unsteady simulation. Finally, the unsteady DDES is performed to predict the propeller
cavitation and URN.
Fig. 3(a) compares the wake-field distribution in terms of the dimensionless axial velocity flowing
into the propeller between the numerical and experimental results. There is good agreement between
the two results. Note that the wakefield is measured in the towing tank, and the numerical simulationis performed for the test section of LCT. The predicted cavitation for volume fraction 𝛼 = 0.1 iscompared with the captured cavitation in the experiment in Fig. 3(b). There is again excellent
agreement between the two results. Fig. 4(a) depicts the pressure perturbation at the stern part. It is

Figure 3– Simulation results and comparison with Exp.; (a) hull wakefield; (b) propeller cavitation.

Figure 4– Simulation results; (a) pressure perturbation on the stern; (b) Comparison of pressure level with
Exp. K2 and K4 (black line – Exp.; red line – Num.)seen that, at the position of the pressure sensors described in Section 3, the pressure perturbationinduced by the convective components is not significant. However, pressure fluctuation due to wave
convection can be clearly seen behind the rudder. Fig. 4(b) compares the hull pressure spectral levels
predicted on the position of K2 and K4 with the measured ones. There are good agreements between
the two results, except for under-predictions at the BPFs.
4.2 Noise analysis results
Noise analysis is performed using the FW-H equation with input from the flow simulation results.
The predicted result is compared with the experimental data. The permeable integral surface for the
FW-H equation is constructed to include the underwater propeller. The sampling frequency (𝑓𝑠 ) is
133,380 Hz, and the Hanning window is applied to prevent leakage errors during signal processing.
The predicted sound pressure spectrum is compared with the measured one in Fig.5. There is excellent
agreement between the two results, except for the under-prediction at the BPFs.

Figure 5– Comparison of predicted noise spectrum using permeable integral surface with Exp.

5. Prediction of URN using hull pressure signal
5.1 Wavenumber-Frequency transform results
The three-dimensional wavenumber-frequency diagram can be calculated for only the rectangularplane. In this study, the curved plane shown in Fig. 6(a) is approximated to be a two-dimensional
rectangular domain, as shown in Fig. 6(b). The Wavenumber-frequency transform is performed using
the surface pressure filed on the stern part. The Power Spectrum Density (PSD) is obtained from thewavenumber-frequency diagram. The volume of the inclined Dirac cone (−𝑐0 + 𝑈0 ≤ 𝜔/𝑘 ≤ 𝑐0 +𝑈0) defined in Eq. (18) includes the compressible components, and the other region is subject to theincompressible components, as shown in Fig. 6(c). The spectrum of compressible and incompressiblepressure is obtained using the following formula.
𝑆(𝜔) = ∫ ∫ 𝑆(𝑘𝑥1 , 𝑘𝑥2 , 𝜔)𝑑𝑘𝑥1 𝑑𝑘𝑥2

(19)

The spectrum obtained through Eq. (19) is shown in Fig. 6(d). The compressible pressure component
is dominant except for the lower low-frequency range.

Figure 6– Wavenumber-frequency transform results; (a) pressure domain on the hull; (b) calculation
domain; (c) 3D wavenumber-frequency diagram; (d) PSD spectrum each component.
5.2 Reflection correction
Since the hull pressure sensor is located on the wall, the reflection of the acoustic wave increases
the pressure magnitude. As the URN is assessed in terms of acoustic power, the compressible pressure
extracted from the wall surface pressure needs to be corrected into the free-field one by consideringwall reflection effects. Because the pressure sensors are located on the curved surface, the soundpressure is not perfectly doubled by the reflection. Therefore, it is necessary to calculate the reflection
correction depending on each position of the curved surface.
The reflection correction value is calculated by the difference between the wall-boundary pressureand free-field pressure calculated from the virtual monopole source located at the same position as
the cavitation observed in the DDES simulation. The Simcenter 3D program is used to calculate theacoustic field due to the monopole source (red-colored sphere) as shown in Fig. 7(a) by using thefollowing formula,𝑒 −𝑖𝑘𝑅(20)
𝑝 = 𝑆̂
𝑅
where 𝑆̂ , 𝑅 , and 𝑘 denote monopole amplitude, distance from the source, and wavenumber,respectively. The reflection correction value is obtained using Eq. (21) below. The reflection
correction in the wavenumber-frequency domain is averaged, as shown in Fig. 7(b).
𝑃𝑤𝑎𝑙𝑙
𝑆𝑃𝐿𝑐𝑜𝑟𝑟 = 20 log10(21)
𝑃𝑓𝑟𝑒𝑒−𝑓𝑖𝑒𝑙𝑑

Figure 7– Reflection correction; (a) boundary condition of Simcenter 3D; (b) averaged reflection correction
on Fig. 6(a).
5.3 Prediction of URN with propagation loss
In addition to the reflection correction, the propagation loss is considered to predict far-field URN.
The equation for propagation loss is as follows,𝑟
𝑃𝐿 = 20 log10(22)𝑟0where 𝑟 and 𝑟0 =1 m are the distance and the reference distance, respectively. Fig. 8 compares the
URN predicted at the position of 1m away from the propeller. It is confirmed that they agree wellwithin a difference of about 1 dB in terms of OASPL.

Figure 8– Comparison of predicted URN between FW-H(1m) spectrum and proposed method result(1m).

6. CONCLUSIONSIn this study, an innovative method was proposed to predict the URN due to the cavitation flow ofa ship propeller by using the surface pressure field as input. The key algorithm of the proposed method
was based on extracting compressible pressure from the surface pressure using the wavenumberfrequency transform and the correction of wall reflection effects. The developed methods were applied
for the KVLCC2 hull and the prototype propeller. The flow simulation results successfully
decomposed the stern pressure into the compressible and incompressible pressure fields through thewavenumber-frequency transform. The URN was then predicted by considering the wall reflection
correction on the curved surface. The acoustic pressure signal predicted using the monitoring method

showed excellent agreement with that obtained from the FW-H equation. This result reveals that thepresent method enables real-time monitoring of the URN of a ship without direct measurement of
acoustic pressure radiated from the ship in the far neighboring sea.

ACKNOWLEDGEMENTS
This work was supported by the Korea Research Institute of Ships and Ocean Engineering (KRISO)
under grant number “PES4280” and the Ministry of Trade, Industry, and Energy (MOTIE) under grant
number “20012974”.

REFERENCES
1. WILLIAMS, Robert, et al. Impacts of anthropogenic noise on marine life: Publication patterns, newdiscoveries, and future directions in research and management. Ocean & Coastal Management, 2015, 115:
17-24.
2. HAWKINS, Anthony D.; POPPER, Arthur N. A sound approach to assessing the impact of underwater
noise on marine fishes and invertebrates. ICES Journal of Marine Science, 2017, 74.3: 635-651.
3. ITTC, The Specialist Committee on Hydrodynamic Noise. 2021
4. AKTAS, Batuhan, et al. Propeller cavitation noise investigations of a research vessel using medium size
cavitation tunnel tests and full-scale trials. Ocean engineering, 2016, 120: 122-135.
5. AHN, Jong-Woo, et al. Comparative study of full-scale propeller cavitation test and LCT model test for
MR tanker. Journal of the Society of Naval Architects of Korea, 2016, 53.3: 171-179.
6. BOSSCHERS, Johan. A semi-empirical prediction method for broadband hull-pressure fluctuations andunderwater radiated noise by propeller tip vortex cavitation. Journal of Marine Science and Engineering,
2018, 6.2: 49.
7. PARK, Cheolsoo, et al. A validation study of the model test method for propeller cavitation noise
prediction. Ocean Engineering, 2020, 213: 107655.
8. FUJIYAMA, Keita; NAKASHIMA, Yoshitaka. Numerical prediction of acoustic noise level induced bycavitation on ship propeller at behind-hull condition. In: Proceedings of the 5th Symposium on Marine
Propulsors, SMP. 2017. p. 739-744.
9. LI, Da-Qing; HALLANDER, Jan; JOHANSSON, Torbjörn. Predicting underwater radiated noise of a fullscale ship with model testing and numerical methods. Ocean Engineering, 2018, 161: 121-135.
10. SEOL, Hanshin; SUH, Jung-Chun; LEE, Soogab. Development of hybrid method for the prediction ofunderwater propeller noise. Journal of Sound and Vibration, 2005, 288.1-2: 345-360.
11. SEOL, Hanshin. Time domain method for the prediction of pressure fluctuation induced by propeller
sheet cavitation: Numerical simulations and experimental validation. Ocean engineering, 2013, 72: 287296.
12. KU, Garam, et al. Numerical Investigation of Tip Vortex Cavitation Inception and Noise of Underwater
Propellers of Submarine Using Sequential Eulerian–Lagrangian Approaches. Applied Sciences, 2020,
10.23: 8721.
13. KU, Garam; CHEONG, Cheolung; SEOL, Hanshin. Numerical investigation of tip-vortex cavitationnoise of an elliptic wing using coupled Eulerian-Lagrangian approaches. Applied Sciences, 2020, 10.17:5897.
14. VANHERPE, Francois, et al. Wavenumber-frequency analysis of the wall pressure fluctuations in thewake of a car side mirror. In: 17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA Aeroacoustics
Conference). 2011. p. 2936.
15. LEE, Songjune, et al. Comparative Analysis of Surface Pressure Fluctuations of High-Speed Train
Running in Open-Field and Tunnel Using LES and Wavenumber-Frequency Analysis. Applied Sciences,2021, 11.24: 11702.
16. BRENTNER, Kenneth S.; FARASSAT, Feri. Analytical comparison of the acoustic analogy andKirchhoff formulation for moving surfaces. AIAA journal, 1998, 36.8: 1379-1386.
17. FARASSAT, Fereidoun. Derivation of Formulations 1 and 1A of Farassat. 2007.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022 in Gyeongju, Korea

ABS-0040

A thermoacoustic heat pump driven by self-sustained oscillations
in a cavity flow with a stack
Hiroshi YOKOYAMA 1; Takahiro MINAMOTO; Masashi KUME;
Masahito NISHIKAWARA; Hideki YANADA
1

Toyohashi University of Technology, Japan

ABSTRACTA thermoacoustic heat pump is driven by aerodynamic sound from cavity flows with a cascade of flat plates
and honeycombs, which are called stacks. The present objective is to clarify the conditions of the cavity flow
and stack for the effective thermoacoustic heat pump. To evaluate the heat pump effects, the temperature
gradient along the stack installed in a rectangular cavity was measured. A higher temperature gradient wasobserved for the cavity flow with the stack of ceramic honeycombs compared with that with stainless-steel
flat plates. Moreover, effective thermoacoustic heat pump phenomena occurred at the specific freestream
velocities, where the intense fluid-resonant oscillations occurred due to the coupling of the shear layer
oscillations and acoustic resonance. The effects of the stack position on the heat pump phenomena were also
discussed.
Keywords: Cavity tone, Thermoacoustics, Heat pump

1. INTRODUCTION

Oscillating flow generated in a gas-filled tube by directing a jet into the open end (Hartman–
Sprenger tube) heats the closed end (1,2). This means that the conversion of acoustic energy to heat
energy can occur, which is called a thermoacoustic heat pump effect. The reduction of aerodynamic
noise radiating from air flows such as cavity flows around side branches and expanded sections ofpipe arrangement in plants is necessary. The utilization of the acoustic energy of aerodynamic noisefor a thermoacoustic heat pump can contribute to both noise reduction and energy harvesting.
A cavity tone, which is the aerodynamic noise generated by the cavity flow, can be an intensesound at a single (fundamental) frequency. Rossiter proposed a feedback loop mechanism with fluid–
acoustic interactions for the generation of the cavity tone (3). In this mechanism, a vortex shed fromthe upstream edge of the cavity collides with the downstream edge; consequently, a generated acoustic
wave propagates to the upstream edge, promoting subsequent vortex shedding. These fluid–acoustic
interactions were confirmed by the numerical simulations (4,5). Recently, the research on utilizationof the acoustic energy of the cavity tone through thermoacoustic phenomena was focused on (6,7).
Regarding the thermoacoustic heat pumps, Wheatley et al. measured the temperature gradientalong a cascade of flat plates (stack) in an acoustically excited resonance tube (8). The largest
temperature gradient was generated when the distance of the stack from the closed end was the oneeighth wavelength of the resonance frequency. It was presented that the fundamental frequency of thecavity tone was also affected by the installation of the stack in the cavity (6). Slaton et al. (7)successfully drove a thermoacoustic heat pump using the cavity tone generated from the flow througha pipe with side branches. They discovered that the ratio of the hydraulic radius of the stack to thethermal penetration depth affected the temperature gradient generated between the stack ends. Also,
simulations for thermoacoustic phenomena driven by cavity tone, which included fluid–acoustic
interactions in the cavity flow and heat conduction in the stack installed in the cavity, were performed(6). As a result, it was shown that the interaction between the recirculation flow in the cavity flow andthe stack deteriorated the thermoacoustic heat pump effects. Therefore, the stack position is an
important parameter for the effective thermoacoustic heat pump by the cavity tone (6,8).
This study aims to clarify the conditions of the cavity flow and stack for an effective
1h-yokoyama@me.tut.ac.jp

thermoacoustic heat pump using the aerodynamic sound from a cavity flow. The effects of the stackposition on the self-sustained oscillations in the cavity flow and thermoacoustic heat pump phenomena
around the stack are focused on.

2. METHODOLOGY
2.1 Flow Configurations
Figure 1 shows the test section including a rectangular cavity in a duct. The origin of the coordinate
is located at the midspan of the upstream edge of the cavity, and the x-, y-, and z-axes are oriented in
the streamwise, normal, and spanwise directions, respectively, as shown in Figure 1. The experiments
were performed in a low-noise suction-type wind tunnel, where the cross-section of the nozzle exit
and duct was 75 mm × 150 mm.
The cavity length and depth were L = 80 mm and D = 280 mm, respectively. The acoustic resonancefrequencies for the first, second and third cavity depth modes, which correspond to one-quarter-, threequarter-, and five-quarter-wavelength modes along the cavity depth, were estimated to be fr = 293,
864, and 1465 Hz. Also, the acoustic mode can occur between the top wall of the duct and the cavity
bottom, which is hereafter called a duct-cavity mode. The duct-cavity mode with one-wavelengthmode was estimated to be 970 Hz. The freestream velocity was varied in the range of U0 = 40 – 85 m/s.
The incoming boundary layer was turbulent, and the boundary layer thickness was 5.2 mm at U0 =80 m/s.

Figure 1 – Schematic of test section in a wind tunnel
2.2 StackA cascade of stainless flat plates (SUS304) and ceramic honeycombs (cordierite), of which thermal
conductivities were 16.3 and 1.5 W/(m･K), respectively, were used as stacks. The hydraulic radius
was r 0 = 0.225, 0.195 mm for the present stainless plates and ceramic honeycombs, respectively. These
values were set to be comparable to the thermal penetration depth of δ α ≡ (α/πfr) 0.5 (α: thermal
diffusivity of air), where r0 /δ α = 1.15 – 3.3, so that the heat conversion between the flow and stack
actively occurred. The position of the vertical center of the stack (stack position) was changed in therange of Hs /D = 0.13 – 0.57 to clarify the effects of the stack position on the thermoacoustic heatpump phenomena and self-sustained oscillations in the cavity flow.
2.3 Measurements
To evaluate the temperature gradient along the stack, the temperature at the stack ends wasmeasured by K-type thermocouples (9810, HIOKI E.E. CORPORATION). In the temperature
measurements, the duration time for data acquisition and the sampling frequency were 600 s and 1 Hz,
respectively. The pressure fluctuations at the cavity bottom (x/L = 0.5, y/D = -1.0) were measured bya pressure sensor (Model8510B-2, Meggitt). The velocity fluctuations in the shear layer (x/L = 0.5,
y/D = -0.11 – 0.09) were measured by a hot-wire anemometer. The duration time for data acquisition
and the sampling frequency were 30 s and 80 kHz, respectively, for measurements of pressure andvelocity fluctuations.

3. RESULTS
3.1 Temperature Gradient along Stack
Figure 2(a) shows the variation of the temperature gradient along the stack ∆T/l s with thefreestream velocity. The temperature gradient became largest around U 0 = 40 and 80 m/s for the stacksof plates (Hs/D = 0.21) and honeycombs (Hs /D = 0.13), respectively. Figure 2(b) shows the maximum
temperature gradient for each stack condition. It is shown that the larger temperature gradient was
generated for the stack of ceramic honeycombs compared with that of stainless plates. The major
reason for this is possibly that the heat conduction in the stack was suppressed due to the lower thermal
conductivity for the ceramic honeycombs. Particularly, the temperature gradient larger than 30 K/m
was observed for the ceramic honeycombs at the position close to the cavity bottom of Hs/D ≤ 0.21.
The maximum temperature gradient of 36 K/m (Hs/D = 0.13) was still lower than that in the literature(7). This is because the present drive ratio of the pressure amplitude to the mean pressure was 0.1%,
which is much smaller than that in the literature but close to the value for actual acoustic radiation inindustrial plants.

(a)

(b)

Figure 2 – Generated temperature gradient. (a) Variation of temperature gradient with freestream velocity.
(b) Variation of temperature gradient with stack position.
3.2 Effects of Stack Installation on Self-Sustained Oscillations
Figure 3 shows the sound pressure spectra at the cavity bottom (x/L = 0.5, y/D = -1.0) for U 0 =Figure 3 – Sound pressure spectra (x/L = 0.5, y/D =Figure 4 – Power spectra of velocity fluctuations in-1.0) for the cavity flow with a ceramic stack

the free shear layer (x/L = 0.5) for the cavity flows

compared with spectrum for the baseline cavity

with a ceramic stack compared with baseline cavity

flow without a stack (U0 = 80 m/s).

flow without a stack (U0 = 80 m/s).

80 m/s for cavity flows with and without ceramic honeycombs as a stack. The horizontal axis is theStrouhal number based on the cavity length and the freestream velocity, St. The tonal sound wasradiated at St = 0.9 for the baseline cavity flow without a stack. The fundamental Strouhal number
was changed to St = 1.1 and 1.5 for the cavity flows with the stack at Hs /D = 0.13 and 0.39, respectively.
These Strouhal numbers approximately correspond to the resonance frequencies for the duct-cavity
mode and for the third cavity depth mode, respectively.
Figure 4 shows the power spectra of the velocity fluctuations in the shear layer (x/L = 0.5) at thevertical position for the most intense velocity fluctuations (baseline, Hs /D = 0.39: y/D = -0.0004, H s/D= 0.13: y/D = -0.0021). The power spectrum for each condition has a peak at the fundamental Strouhal
number of the acoustic radiation. This indicates that fluid-resonant oscillations (9) occurred by the
coupling between the shear layer oscillations and above-mentioned acoustic resonance. As shown in
Figures 3 and 4, both the sound pressure level and the power of velocity fluctuations at thefundamental Strouhal number were decreased by the installation of the stack. This means the
suppression of the self-sustained oscillations in the cavity flow.

4. CONCLUSIONSTo clarify the conditions of the cavity flow and stack for an effective thermoacoustic heat pumpusing the aerodynamic sound from a cavity flow, wind tunnel experiments were performed. The
temperature gradient along the stack became largest at the specific freestream velocity, where thefluid-resonant oscillations occurred. Particularly, the temperature gradient larger than 30 K/m wasobserved for the ceramic stack installed at the ratio of the distance from the cavity bottom to the cavity
depth of less than around 20%. However, the investigation for the stack closer to the cavity bottom
was necessary in the future, while the lowest stack position was 13% in the present study. The
installation of the stack affected the occurring acoustic mode in the cavity. The reduction of soundpressure level and velocity fluctuations by the stack installation indicates the suppression of the selfsustained oscillations in the cavity flow. In addition to the noise reduction, the obtained temperature
gradient can be also converted to electric power through a thermoelectric element, which contributes
to energy harvesting.

ACKNOWLEDGEMENTS

This work was supported by MEXT as a Program for Promoting Research on the Supercomputer“Fugaku” (hp200123, hp200134), and JSPS KAKENHI 21K03874.

REFERENCES

1. Sprenger H. Beobachlungen an Wirbelrohren. J Appl Math Phys (ZAMP). 1951;2:293–300.
2. Kawahashi M, Suzuki M. Temperature separation produced by a Hartmann-Sprenger tube coupling asecondary resonator. Int J Heat Mass Transfer. 1981;24(12):1951–1958.
3. Rossiter JE. Wind-tunnel experiments on the flow over rectangular cavities at subsonic and transonic
speeds. Aeronautical Research Council Reports and Memoranda. 1964;3438.
4. Rowley CW, Colonius T, Basu AJ. On self-sustained oscillations in two-dimensional compressible flow
over rectangular cavities. J Fluid Mech. 2002;455:315–346.
5. Yokoyama H, Kato C. Fluid-acoustic interactions in self-sustained oscillations in turbulent cavity flows:
I. Fluid-dynamic oscillations. Phys Fluids. 2009;21(10):105103.
6. Yokoyama H, Omori Y, Kume M, Nishikawara M, Yanada H. Simulation of thermoacoustic heat pumpeffects driven by acoustic radiation in a cavity flow: Int J Heat Mass Transfer. 2022;185:122424.
7. Slaton WV, Zeegers JCH. An aeroacoustically driven thermoacoustic heat pump: J Acoust Soc Am
2005;117:3628–3635.
8. Wheatley J, Hofler T, Swift GW, Migliori A. Experiments with an intrinsically irreversible acoustic heatengine. Phys Review Letters. 1983;50(7):499–502.
9. Rockwell D, Naudascher E. Review—self-sustaining oscillations of flow past cavities. Trans ASME: J
Fluids Eng. 1978;100:152–165.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022, in Gyeongju, Korea
Extended abstractABS-0698

Optimization of TiO2 Photocatalytic Activity Using Focused
Ultrasound System and Degradation of Organic Dyes
Soyul Kim1,2 ; So Young Kim1; Jong Ryul Jeoung2; Seon Ae Hwangbo1*
1
2

Nano Safety, Korea Research Institute of Standards and Science , Korea

Materials Science and Engineering, CHUNGNAM NATIONAL UNIVERSITY, Korea

ABSTRACTTiO2 has a photocatalytic property in which organic matter react with electrons and holes in a separated
state. This property is mainly used in nano-size because the larger the surface area of the particles, the more
likely it occurs. For this purpose, the particles must be dispersed. However, the particles size is small,aggregation is increased.
The focused ultrasound system disperses particles without using a surfactant. The driving principle of thissystem is that when ultrasound are applied to cylindrical piezoelectric ceramics, energy is focused to thecenter. This energy is applied to numerous microbubbles in the water flowing through the system, and as the
bubble collapses, it gives energy around it, dispersing the particles in nano-size.
In this study, the photocatalytic activity of TiO2 before and after ultrasonic dispersion in methylene blue
was compared.
Keywords: Nano particles, Micro particles, Ultrasound, Dispersion

1. INTRODUCTION
Methylene blue is a dye that does not easily decompose. Therefore, research is underway on how
to decompose methylene blue, of which the photolysis process removes the chromaticity of dye
molecules by a highly reactive material such as hydroxyl radicals and finally decomposes them into
H2O and CO 2.[1]Titanium dioxide is a representative photocatalytic material used in the photolysis reaction of
methylene blue. [2] In the optimization process of the photolysis process, the size of TiO 2 is one of
the main factors affecting resolution. As the particle size decreases to the nano -sized level, the areaof the surface on which the photocatalytic properties are activated increases. [1] Since this ultimately
affects the decomposition of methylene blue, it is judged that the photocatalytic material has higher
photocatalytic activity when it is in the form of nanoparticles. Since the photolysis reaction of TiO 2
is affected by the size and distribution of particles [3-5], the optimal nano-size conditions fordecomposing the dye must be satisfied.
However, in nanoparticles, the attraction between the particles is strong due to the van der Waals
force, and accordingly, the aggregation of the particles occurs. [6] Surfactants or the like are used tocontrol this. This can cause not only production costs but also additional environmental pollution. In
the method of physically dispersing nanoparticles, the dispersion is contaminated and th e particles are
not uniformly dispersed.[7, 8] Therefore, the ultrasonic dispersion system is attracting attention as adispersion method of nanoparticles. Therefore, in this experiment, a focused ultrasonic system wasused while adopting a non-contact ultrasonic dispersion. [9]winnie5541@kriss.re.kr
soyoung3680@kriss.re.kr
3
hbsa@kriss.re.kr
12

2. RESULT AND DISCUSSION
2.1 Effect of Size at Photodegradation
An experiment was conducted on the effect of the size of the particles controlled by thenanoparticle size on the degradation of methylene blue.
Table 1. Degradation % when UV exposure time is 40 min for each sample
SampleSize (μm)

UV Exposure Time (min)Degradation (%)

1

3

40

78.5

2

0.117

40

84.1

3

0.075

40

84.6

In Table 1, it can be seen that the colloidal particles of 3 μm, 107nm, and 75nm show degradationof 78.5%, 86.5%, and 84.6% when irradiated with ultraviolet rays for nearly 40 minutes, respectively.
In this case, when the photolysis reaction of the colloid dispersed in the nano -size is performed for 40
minutes, the resolution of the particles whose particle size is controlled in the nano -size region issuperior to that of the micro-sized TiO2. Therefore, it can be concluded that adjusting the size of the
TiO2 particles affects the resolution of dyes such as methylene blue.

3. CONCLUSION
In this study, the difference in photocatalytic activation according to the size of TiO 2 particles inthe degradation of methylene blue was studied. In order to reduce the particle size, a focused ultrasonicsystem was used, which was useful as a particle dispersion device. In addition, a methylene blue
degradation experiment was conducted using particles dispersed with this equipment. As a result, it
was confirmed that the TiO 2 particles, whose agglomeration size is controlled to a nano -size, havebetter photolysis activity in methylene blue than the micro-sized particles.

REFERENCES
1. . I Khan, K Saeed, I Zekker, B Zhang, AH Hendi, A Ahmad, S Ahmad, N Zada, H Ahmad, LA Shah,
Review on methylene blue: its properties, uses, toxicity and photodegradation. Water 14, 242 (2022).
doi:10.3390/w14020242
2. S Ali, SA Khan, I Khan, ZH Yamani, M Sohail, MA Morsy, Surfactant-free synthesis of ellipsoidal andspherical shaped TiO2 nanoparticles and their comparative photocatalytic studies. J. Environ. Chem. Eng.
5, 3956–3962 (2017). doi:10.1016/j.jece.2017.07.066.
3. F Pellegrino, L Pellutié, F Sordello, C Minero, E Ortel, VD Hodoroaba, V Maurino, Influence of
agglomeration and aggregation on the photocatalytic activity of TiO2 nanoparticles, Appl. Catal. B
Environ. 216, 80–87 (2017). doi:10.1016/j.apcatb.2017.05.046.
4. W Zhang, H Tang, Rutile nanopowders for pigment production: formation mechanism and particle size
prediction. Chem. Phys. Lett. 692, 129–133 (2018). doi:10.1016/j.cplett.2017.12.025
5. M Safiuddin, M Gonzalez, J Cao, SL Tighe, State-of-the-art report on use of nanomaterials in concrete,
Int. J. Pavement Eng. Asph. Technol. 8436, 1–10 (2014). doi:10.1080/10298436.2014.893327
6. K Sato, JG Li, H Kamiya, T Ishigaki, Ultrasonic dispersion of TiO2 nanoparticles in aqueous suspension.
J. Am. Ceram. Soc. 91, 2481–2487 (2008). doi:10.1111/j.1551-2916.2008.02493.x
7. S Sumitomo, H Koizumi, M Azhar Uddin, Y Kato, Comparison of dispersion behavior of agglomerated
particles in liquid between ultrasonic irradiation and mechanical stirring. Ultrason. Sonochem. 40, 822–
831 (2018). doi:10.1016/j.ultsonch.2017.08.023
8. M Inkyo, T Tahara, T Iwaki, F Iskandar, CJ Jr. Hogan, K Okuyama, Experimental investigation of
nanoparticle dispersion by beads milling with centrifugal bead separation. J. Colloid Interface Sci. 304,
535–540 (2006).
9. SA Hwangbo, M Kwak, JKim, TG Lee, Novel surfactant-free water dispersion technique of TiO2 NPs
using focused ultrasound system. Nanomaterials. 11, 427 (2021). doi:10.3390/nano11020427.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022, in Gyeongju, Korea
Extended abstractABS-0699

A study on the manufacturing method of calibration materials for
medical imaging devices using focused ultrasound system
JiYun Lee1; JiSoo Yun2; JinKee Hong3; SeonAe Hwangbo4
1

Nanosafety Team, KRISS, Korea; Chemical and Biomolecular Engineering, Yonsei University, Korea
2
3

Nanosafety Team, KRISS, Korea

Chemical and Biomolecular Engineering, Yonsei University, Korea
4

Nanosafety Team, KRISS, Korea

ABSTRACTMRI is the medical system that can obtain arbitrary tomography images of living organisms using magnetic
fields generated by magnetic force, and can diagnose diseases by measuring electromagnetic waves echoedby transcribing high frequencies to the human body in strong magnetic field. However, when measuring theamount of fat in the body with MRI, each equipment manufacturers has a different value.
As the calibration material for medical imaging devices for accurate MRI image analysis, the lipid emulsionbased phantom is manufactured. Surfactants generally used to improve stability in emulsion make it difficult
to accurately analyze the fat fraction in the body in the analysis of imaging devices such as MRI. Therefore,
the emulsion without using a surfactant is manufactured using the focused ultrasonic system.
The ultrasonic energy is focused to the center through that the sample passes using cylindrical piezoelectric
ceramic. When repetitive sound pressure is applied due to ultrasonic waves, cavitation bubbles increase andcollapse. The energy generated by this collapse can emulsify oil in water.
For stable use of emulsion, particle size and dispersion stability analysis were performed at high temperatures.
In addition, MRI image analysis was conducted for each cycle of samples given in harsh environments.
Keywords: Emulsion, Emulsion Stability, Surfactant-free, MR phantom

1. INTRODUCTION
Magnetic Resonance Imaging (MRI) diagnoses diseases by photographing images of cross-sections ofmuscles, cartilage, blood vessels, and nerves using magnetic properties and electromagnetic waves ofmaterials that compose the human body. So far, many researchers have verified and compared MRI-based
water and fat quantification methods to study MR (Magnetic Resonance) signal changes in oil and water inemulsions [1-8]. However, when measuring the amount of fat in the human body using MRI, the equipment
shows different measurements for each manufacturer of the equipment. Large errors represented byequipment manufacturers reduce reliability in measurements and make accurate diagnosis of diseases
impossible. In order to accurately diagnose the disease, there is a need for a method that can present an error
value for the measurement of MR. Therefore, reliable measurement phantoms are essential for testing MRI
equipment, and composition and production have become important research areas [9-12].
To this end, the MR phantom emulsion made of water and oil is prepared. The human body is mainlycomposed of water and oil, so oil-in-water emulsion acts appropriately for simulation of in vivo conditions.
Emulsion refers to a solution in which a liquid is spread in a colloidal state in another liquid, and occurs
wldbs@kriss.re.kr
jisoo991208@kriss.re.kr
3
gf@ccc.go.jp [Please note: It is optional to provide the email address(es) of the author(s). Please make surethat your co-authors concur with the mention of their email address in this paper.]1
2

4

hbsa@kriss.re.kr

between two liquids that do not mix [13, 14]. The emulsion is thermodynamically unstable. Due to thecharacteristics of lipids with hydrophobicity and high interfacial tension, emulsions are separated into purewater and oil immediately after preparation. Surfactants (emulsifiers) with amphiphilic molecular structures
are added for stable emulsion. The addition of a surfactant makes it difficult to measure an accurate value in
MR measurement [15]. Therefore, research on emulsion production without adding a surfactant is essential.
The size of the oil droplets in the emulsion effects the emulsion stability. It is used the focusedultrasonic system do disperse oil without surfactant. For stable emulsion, the focused ultrasoundsystem perform emulsification with oil and water. In the focused ultrasonic technology, the acoustic
energy is directed from the cylindrical piezoelectric ceramic to the center of the system through which
the sample passes. As cavitation occurs due to repeated negative pressure energy, bubbles gradually
increase. The larger bubbles are destroyed at the threshold, and the energy generated at this timedepends on the frequency, temperature, power, and viscosity [16]. Emulsification is performed bydispersing uniformly injected oil in water using this energy. It is very strong energy and can disperse
the material without additional surfactants or additives.
In addition, gelling agents are added to using stable emulsion. The addition of gelling agents gives various
properties such as increased viscosity, lubrication, and emulsification. There are four types of gelling agents,and each gelling agent is added to the emulsion.

2. Material and Method
2.1. Preparation of MR Phantom Emulsions
In order to prepare an emulsion phantom for MR phantom, distilled water and grape seedoil(DAYDAYTHERAPY) were used. In the prepared emulsion, the ratio of oil/water phase was
20/80%.
The ultrasonic energy focuses to the center of the cylinder through that the sample passes using
cylindrical piezoelectric ceramic, and emulsification is performed. It is injected oil at a constant rateby a syringe pump, passed through the PZT with water, and an emulsion is prepared. It is used thatfrequency at 400 kHz and power of 150 W.
When the gelling agent was added, different contents were added for each type of gelling agent to
prepare an emulsion of similar viscosity. The process of adding the gelling agent was shown in Table
1.
Table 1
Gelling Agent

Content [wt%]

Xanthan gum

1.0

Carbopol 981

1.0

Pemulen TR-2

0.5

Carbopol Ultrez 20

0.5

Mixing 1

Mixing 2

Defoaming

8000 rpm and for 20 min with gelling agent

8000 rpm,
20 min withneutralizer

180 s

After Soaking gelling agent 10 min, mixing 8000 rpm for 20 min

2.2. Characterization of Emulsion
For high temperature stability analysis, measurements were performed while storing emulsion at
45 °C. In order to analyze the change in emulsion size at high temperature, size measurement was
performed using Laser Particle Size Analyzer (LA-960, HORIBA) every week for a month. Light isscattered in different patterns by the size of the particle. LA-960 uses these Mie scatterings to calculate
the size. Measurements of the correct size are performed using two wavelength -banded light sourcesof 650 nm and 405 nm. Each sample was diluted 100 times with distilled water to measure the size.
For size distribution analysis, the sample was measured by making the transmittance of the blue lightsource (405 nm) equal to 86 to 85%.

3. Result & Discussion
3.1 High Temperature Stability
For high temperature stability analysis, the particle size distribution were measured immediately
and 1 month after the emulsions had been prepared. Immediately after manufacture in the case ofemulsion with xanthan gum was shown the largest size of emulsion in tens of micrometers. Except forxanthan gum, the size of the emulsions with other gelling agents was measured in several micrometers.
In the case of Ultrez 20 and TR-2, which prepared 0.5 and 0.25 wt % gelling agent contents according
to viscosity, more uniform and small sizes were measured in the emulsions having a high gelling agent
content of 0.5 wt %.
To measure the emulsion stability of the emulsions in a high-temperature environment, it wasstored at 45 ℃. In the case of xanthan gum and carbopol 981, there was a large change in size. Sizeof emulsions with xanthan gum (1.0 wt%) grew to more than 2.2 μm. In addition, size of emulsion
with carbopol 981 (1.0 wt%) showed a size change of about 6 μm. On the other hand, in the case of
the emulsions to which TR-2 and Ultrez 20 were added, all four emulsions did not show change insize for a month at high temperature (45℃). Since there was no size change even in the emulsions
added gelling agent of low concentration, it was confirmed that the stable emulsion can be
manufactured even with a small amount of TR-2 and Ultrez 20.
(a)

(b)

Fig. 1. Particle size distribution of emulsions by gelling agents: (a) 1day, and (b) 1 month

4. Conclusion
In this study, a stable emulsion was produced with surfactant-free emulsification technique for MR
phantom preparation. A stable emulsion was prepared using focused ultrasonic technology, and gelling
agents were added to provide additional stability. Stability tests were performed at high temperatures
for exposure to various environments. The size of the emulsion was measured while being stored at
45 ℃ for a month. In the case of an emulsion to which xanthan gum and carbopol 981 were added,
when stored at a high temperature for a month, it was confirmed that the size incre ased by 6 µm and2.2 µm, respectively, to be unstable. In the case of the emulsion to which TR -2 and Ultraz 20 wereadded, it was confirmed that the size was not changed for a month, so it was very stabl e. However, inthe case of Ultrez 20, the viscosity increased significantly despite the addition of a small amount. Thismay be a problem for uniform sampling of emulsion. Therefore, it was confirmed that Pemulen TR-2
was the most suitable gelling agent in MR phantom manufacturing. The selected TR-2 will allow
emulsion, which can be exposed to various environments, to maintain high stability and enableuniform oil distribution.

ACKNOWLEDGEMENTS
Authors may acknowledge financial or other forms of support in this Section. All
acknowledgements shall be placed after Conclusions and before References. Numerically ordering is
not necessary for the “ACKNOWLEDGEMENTS” or “REFERENCES” headings, which should usethe pre-defined style “Major without number.”

REFERENCES
Tadros, T. F. (2013). Emulsion formation, stability, and rheology. Emulsion formation andstability, 1, 1-75.
2. Chen, G., & Tao, D. (2005). An experimental study of stability of oil–water emulsion. Fuelprocessing technology, 86(5), 499-508.
3. Gursoy, R. N., & Benita, S. (2004). Self-emulsifying drug delivery systems (SEDDS) for improved
oral delivery of lipophilic drugs. Biomedicine & pharmacotherapy, 58(3), 173-182.
4. Kohli, K., Chopra, S., Dhar, D., Arora, S., & Khar, R. K. (2010). Self-emulsifying drug delivery
systems: an approach to enhance oral bioavailability. Drug discovery today, 15(21-22), 958-965.
5. Singh, B., Bandopadhyay, S., Kapil, R., Singh, R., & Katare, O. P. (2009). Self-emulsifying drugdelivery systems (SEDDS): formulation development, characterization, and applications. Critical
Reviews™ in Therapeutic Drug Carrier Systems, 26(5).
6. Kumar, M., Bishnoi, R. S., Shukla, A. K., & Jain, C. P. (2019). Techniques for formulation of
nanoemulsion drug delivery system: A review. Preventive nutrition and food science, 24(3), 225.
7. Israelachvili, J. N. (2011). Intermolecular and surface forces. Academic press.
8. van der Schans, C. P., Postma, D. S., Koeter, G. H., & Rubin, B. K. (1999). Physiotherapy andbronchial mucus transport. European Respiratory Journal, 13(6), 1477-1486.
9. Zhao, H., Kang, W., Yang, H., Huang, Z., Zhou, B., & Sarsenbekuly, B. (2021). Emulsification andstabilization mechanism of crude oil emulsion by surfactant synergistic amphiphilic polymer
system. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 609, 125726.
10. Yin, N., Chen, K., & Kang, W. (2006). Preparation of BA/ST/AM nano particles by ultrasonicemulsifier-free emulsion polymerization. Ultrasonics sonochemistry, 13(4), 345-351.
11. Hwangbo, S. A., Lee, S. Y., Kim, B. A., & Moon, C. K. (2022). Preparation of Surfactant-Free Nano
Oil Particles in Water Using Ultrasonic System and the Mechanism of Emulsion
Stability. Nanomaterials, 12(9), 1547.
12. Kaci, M., Meziani, S., Arab-Tehrany, E., Gillet, G., Desjardins-Lavisse, I., & Desobry, S. (2014).
Emulsification by high frequency ultrasound using piezoelectric transducer: Formation and stabilityof emulsifier free emulsion. Ultrasonics sonochemistry, 21(3), 1010-1017.
13. Bramhe, S. N., Park, J. Y., Hwangbo, S. A., & Chu, M. C. (2016). Facile synthesis of surfactantfree SiO2 nanoparticles via emulsion method. Advanced Powder Technology, 27(6), 2541-2545.
14. Kaci, M., Arab-Tehrany, E., Desjardins, I., Banon-Desobry, S., & Desobry, S. (2017). Emulsifier
free emulsion: Comparative study between a new high frequency ultrasound process and standard
emulsification processes. Journal of Food Engineering, 194, 109-118.
15. Glicksman, M. (Ed.). (2020). Food hydrocolloids (Vol. 3). Crc Press.
16. Hwangbo, S. A., Kwak, M., Kim, J., & Lee, T. G. (2021). Novel surfactant-free water dispersion
technique of TiO2 NPs using focused ultrasound system. Nanomaterials, 11(2), 427.
1.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022 in Gyeongju, Korea

ABS-0773

Numerical and experimental investigation for suppression of
narrow-gap flow whistle of automobile side-mirror with guide-rib
Kwongi Lee1; Songjune Lee1; Sangheon Lee1; Cheolung Cheong1,*; Sungnam Rim2; Seongryong
Shin22
1

School of Mechanical Engineering, Pusan National University, Pusan 46241, Republic of Korea
2

Hyundai Motor Company, Hwaseong-si 18280, Republic of Korea

ABSTRACT
It is frequently reported that the high-frequency tonal noise, the whistle, is generated by airflow through thenarrow-gap of a vehicle’s side-view mirror. The present study aims to identify the generation mechanism of
the narrow-gap whistle of a side-view mirror and to suppress it by eliminating the recognized primary sources.
The wind tunnel test was performed to identify the geometric features contributing to the whistle and theflow conditions for the onset of the whistle. The simplified side-view mirror model (SSM) was devised forflow visualization by employing the identified geometric features of the narrow-gap. Flow structures of the
SSM were visualized using the oil smog and high-speed camera. The numerical simulation of the internaland external flows of the SSM was conducted by using the compressible LES techniques to identify thegeneration mechanism of the narrow-gap whistle. The simulation was validated by comparing the numericalresults of the main flow structure and the sound pressure spectrum with the measured ones. The primary
aerodynamic sources were identified using the vortex sound sources, and the generation mechanism wasshown to be related to the edge tone. Finally, it is shown that the vortex generator introduced to eliminate theidentified whistle’s sources successfully suppressed the narrow-gap whistle.
Keywords: Whistle sound, Side-mirror, vortex sound source, Large Eddy Simulation, Vortex generator

1. INTRODUCTION
As the traditional vehicle noise due to combustion engines decreases and even disappears inelectric vehicles, whose sales and production are rising, the relative importance of aerodynamic noise
becomes increasingly significant. One of the major aerodynamic sound sources of the car is a sidemirror due to its extruded discontinuous geometry. When a vehicle runs over 70 km/h, a tonal noisefrom a narrow-gap in the side-mirror has been frequently reported to cause an inconvenience to thedriver, called a ‘whistle.’ However, because this type of whistle is generated from a narrow-gap of
about 1 mm, the experimental and numerical investigation for identifying the generation mechanismof the whistle sound is very challenging.
Chanaud[1] classified the aerodynamic whistle into three classes according to a feedback
mechanism: near-field, intermediate and far-field feedback. Lounsberry et al.[2] experimentallyinvestigated laminar-flow whistling over a side-mirror housing of an automobile and showed that theboundary layer starts as laminar and attempts to change to turbulent, fluctuating at a high frequency.
Flow visualization results confirmed the laminar separation region on the side-mirror case. Werner etal.[3-4] experimentally studied the tonal noise on a side-mirror through flow visualization using the
PIV. An instability by the shear layer starting from the side-mirror housing causes the aeroacoustic
feedback loop known as the generation mechanism of self-noise emission over the airfoils. Hannes et1

dlrnjsrl93@pusan.ac.kr(K.L.); sjlee@pusan.ac.kr(S.L.); tkdwjdwjd222@pusan.ac.r(S.L.)

1,* ccheong@pusan.ac.kr
2

4everwithu@hyundai.com(S.R.); ssdradon@hyundai.com(S.S.)

al.[5] directly simulated acoustic feedback phenomena on a side-mirror using high-order schemes.
The mode decomposition and instability analysis were conducted to figure out the generation
mechanism of the whistle sound. However, all of these works [2-5] focused on the tonal noise
generation by the external flow over side-mirrors but not the internal narrow-gap flow.
Miguel et al.[6] analyzed a tonal noise from the airfoil through nonlinear numerical simulations
and made a global stability analysis for identifying a feedback mechanism. Masataka et al. [7]investigated a feedback mechanism of an air-reed instrument using a compressible LES technique.
They numerically visualized the Lighthill’s sound source and observed the frequency-locking
phenomena. Although the characteristics of the airfoil and air-reed instrument are different from thatof narrow-gap flow through a side-mirror, the methods employed in these studies were used in thepresent study.
Velte et al.[8] utilized a vortex generator to reduce the tonal noise from an airfoil. A vortex structure
induced by the vortex generator broke the original large coherent vortex structures. This concept was
utilized to devise a measure to suppress the whistle sound generated by the internal flow through thenarrow-gap in a side-mirror.
Lee et al.[9] investigated the whistle sound generation from the narrow-gap flow through aconventional side-mirror and clearly visualized the standing wave of compressible pressure field
coupled with the hydrodynamic pressure fluctuation, which revealed that an acoustic feedback
mechanism is involved in generating the whistling sound.
A guide-rib was introduced to the inlet flow passage of the narrow-gap of the conventional sidemirror to eliminate the whistle sound, but the whistle sound still exists at a higher frequency. This
study investigates the generation mechanism of the whistling sound from the side-mirror with theguide-rib. Different from the conventional side-mirror, the identified mechanism was due to instabilityby the shear layer with a separation, which occurred at the trailing edge of the guide-rib. In the end,a measure was suggested to suppress the whistle sound.

2. EXPERIMENTAL METHODS
2.1 Sound Measurement
An experiment of whistle sound measurement is conducted to find the flow conditions when thewhistling sound is generated by the narrow-gap flow of an automobile side-mirror and to characterize
the frequency spectrum of whistle sound. Figure 1 shows the experimental configuration formeasuring the aerodynamic noise from airflow passing through a narrow-gap of the side-mirror. A
small wind tunnel is used to drive airflow through the side-mirror. A microphone to record thewhistling sound is located at the position of which the distance from the side-mirror matches the
distance between a driver and a side-mirror. The detailed conditions for the whistle soundmeasurement and post-processing are shown in Table 1.

Figure 1 – Experimental setup for measurement of whistling sound due to airflow through vehicle sidemirror: (a) diagram of the entire experimental system, (b) photograph taken from the side, and (c) real-scale
photograph taken from the top.
Table 1 – Detailed settings of sound measurement.
Sound Measurement

Type & Settings

Microphone

Bruel & Kjaer 4189

Measurement Time

10 sec.

Sampling Frequency

40960 Hz

Frequency Resolution

1 Hz

Overlap

70 %Window

Hanning

Reference pressure

20 PaWeightingA-weighting

2.2 Flow Visualization
A flow visualization experiment for capturing the flow structures in narrow-gap contributing to thegeneration of the whistle is conducted. Figure 2 shows the schematic diagram of the experimental
setup for flow visualization and the picture taken during the experiment. The airflow with oil smog isdriven to enter the narrow-gap of the simplified side-mirror model (SSM) made of transparent acrylic
material. The geometric feature of SSM is described in detail in the Section 3.2 and 3.3. When thewhistle sound is identified through the microphone, the He-Ne LASER and the high-speed camera areutilized to visualize the related flow structures through the narrow-gap of the SSM. The frame persecond of the high-speed camera was 20,000 Hz.

Figure 2 – Experimental setup for visualization of narrow-gap flow through simplified side-mirror model(SSM): (a) schematic diagram of entire experimental system and (b) photograph taken from side.

3. EXPERIMENTAL RESULTS
3.1 Identification of Whistle
Based on the analysis result of the conventional side-mirror by Lee et al. [9], an obstacle called‘guide-rib’ was adopted to prevent the generation of a whistling sound. However, another whistlingsound was found to occur at different frequencies. The primary purpose of the present study is to findthe generation mechanism of whistle sound and to devise a measure to eliminate it. Figure 3 shows
the geometries in the narrow-gap of the target side-mirror. Various holes and gaps of complex shapes(red-dashed circles) and the guide-rib exist in the narrow passage, as shown in Figure 3a. The
preliminary experiments were conducted to assess these complex shapes' effects on the generation ofwhistle sound. Based on these experiments, the simplified side-mirror was obtained by eliminatingthese holes and gaps, as shown in Fig. 3(b)Figure 4 shows the sound pressure spectrums obtained for the original side-mirror in various flow
velocities. When the flow velocities are varied from 17 m/s to 26 m/s, the tonal components of
bandwidth wider than 100Hz occurred at the flow velocities higher than 17 m/s. These components
are defined as the whistle sound. The other tonal components at 3000 Hz, 6000 Hz, and 9000 Hz are
due to the motor driving the small wind tunnel. When the flow velocity is 17m/s, that the whistle
sound is absent was unclear due to motor sound at 6000Hz.

Figure 3 – Shape of target automobile side-mirror: (a) original side-mirror and (b) simplified side-mirror(SS).

Figure 4 – Sound pressure spectrum of side-mirror at various flow speeds.
Simplified Side-mirror Model
Because the shape of the narrow-gap in the side-mirror is very complex, the original side-mirror
shape needs to be simplified to make it easier to identify the main structural part causing the whistle
sound through the flow visualization experiment and numerical analysis. The holes and gaps areblocked one by one, as shown in Fig. 3(b), and the radiated noise spectra are measured, which reveals
that these geometries did not contribute to the whistle sound. The side-mirror was finally obtained inthis way, shown in Fig. 3(b), and named ‘Simplified Side-mirror (SS).’ The sound measurement
experiment was conducted for the SS. Figure 5 compares the sound spectra measured for the originalside-mirror, the SS, and the Simplified Side-mirror Model (SSM). The SSM is designed to reproduce
only the flow passage of the SS and is made of transparent acrylic material for flow visualization, as
shown in Fig. 6. It can be seen that the spectra of the original one and SS are similar, and the whistle
sound component exists between 7000Hz and 8000Hz. The sound spectrum measured for the SSM
shows the whistle component at a frequency identical to the original side-mirror and SS, although its
spectral levels are lower than the others. These lower levels can be expected from the fact that theexternal shape of SSM is a simple flat plate. Overall, the frequency of the maximum whistling soundlevel of the SSM is slightly different, but the whistle sound occurs at a similar frequency, implyingthat the SSM's internal flow reflects the side-mirror's narrow-gap flow feature causing the whistle
sound.
3.2

Figure 5 – Comparison of sound pressure spectra measured for original side-mirror, simplified
side-mirror (SS), and simplified side-mirror model (SSM) at a flow speed of 22 m/s.

Figure 6 – Geometry of simplified side-mirror model (SSM): (a) transparent acrylic sample, (b)CAD of SSM, and (c) main geometric features.

4. NUMERICAL METHODS
4.1 Large Eddy Simulation
Because the purpose of this study is to investigate the generation mechanism of whistle sound fromthe narrow-gap flow, the compressible Large Eddy Simulation (LES) technique combined with highresolution grids was used to numerically reproduce the generation of whistle sound by the vortex
sound source in narrow-gap and its propagation through and out of narrow-gap. The computation
domain is constructed to include the sound propagation regions so that the radiated sound pressure isdirectly computed at the same position as the sound measurement location.
The three-dimensional unsteady compressible LES technique with Wall-Adapting Local EddyViscosity (WALE) sub-grid model can be written in the form below:𝜕𝜌 𝜕+ (𝜌𝑢̅𝑖 ) = 0
𝜕𝑡 𝑥𝑖

(1)

𝜕𝜏𝑖𝑗
𝜕
𝜕
𝜕𝑝̅
𝜕
𝜕𝑢̅𝑖 𝜕𝑢̅𝑗(𝜌𝑢̅𝑖 ) + (𝜌𝑢̅𝑖 𝑢̅𝑗 ) = −
+
[𝜇 (
+
)] −
𝜕𝑡
𝑥𝑗
𝜕𝑥𝑖 𝜕𝑥𝑗𝜕𝑥𝑗 𝜕𝑥𝑖
𝜕𝑥𝑗

(2)

𝜕
𝜕
𝜕
𝜕𝑢𝑖 𝜕𝑢𝑗(𝜌̅ 𝐸) + (𝜌̅ 𝑢𝑗 𝐻) =+) − 𝑝))] + ̅̅̅̅̅̅̅
𝑢𝑖 ′𝜎𝑖𝑗[(𝑢𝑗 (𝜇 (𝜕𝑡𝑥𝑗𝜕𝑥𝑖𝜕𝑥𝑗 𝜕𝑥𝑖
𝜕 𝑐𝑝 𝜇 𝜕𝑇
1 ̅̅̅̅̅̅̅̅̅̅̅̅
̅̅̅̅̅̅̅̅̅
−[+ 𝑐𝑝 ̅̅̅̅̅̅̅
𝜌𝑢𝑗′ 𝑇 ′ + 𝑢𝑖 𝜌𝑢𝑖 ′𝑢𝑗 ′ + 𝜌𝑢𝑖 ′𝑢𝑖 ′𝑢𝑗 ′] ,𝜕𝑥𝑗 𝑃𝑟 𝜕𝑥𝑗
2(3)

where 𝜎𝑖𝑗 is the stress tensor due to molecular viscosity and 𝑖𝑗 is the subgrid-scale stress tensor
based on the Boussinesq hypothesis.
The numerical computation domain is constructed to reproduce the experimental setup formeasuring the whistle sound owing to the narrow-gap flow of the side-mirror. The SSM described in
Section 3.2 is targeted for the current numerical analysis since the measured sound spectrum , and thevisualized flow field are available for comparison with the numerical results. Figure 7 shows the entire
numerical domain with related dimensions and applied boundary conditions. The velocity inlet,pressure outlet, and far-field pressure conditions are used as the boundary conditions. Table 2 shows
the detailed values of the boundary conditions. The inlet velocity is set as 22 m/s, the proper flow
velocity of the experiments described in Section 3.2. The non-reflecting condition is applied to theinlet and outlet boundary conditions to suppress the possible contamination of sound waves in thecomputational domain due to a reflected wave from the boundaries.
The transient LES simulation was conducted with initial conditions obtained from a steady RANS
result to get reliable unsteady data. To ensure convergence, the data after 0.7 seconds is used for
subsequent analysis. Note that it takes 0.068 seconds for the inlet flow to arrive at the outlet boundary.
The time step size is set as 1/160,000 seconds, meaning that the 20 points of time data constitute one
period of the whistle sound of 8,000 Hz. The total time length of the unsteady pressure data at theobserver point is 0.1 seconds, which matches the frequency resolution of 10 Hz. However, theunsteady flow field is recorded for 0.01 seconds for fast and cost-effective post-processing.
Figure 8 shows the computational grids of high resolutions enough to capture and reproduce thewhistle sound. In the sound propagation region which is inside a sphere of radius 0.3 m but outside
the SSM, the maximum grid size is 4 mm, implying that twenty grid points constitute one wavelengthof the whistling sound at 8,000 Hz. Figures 8-(b), -(c), and -(d) show the zoomed views of meshes onthe vertical cross-section plane around the guide-rib and inside the cavity and on the horizontal crosssection plane of the stopper inside the cavity, respectively. In the sound source region of the narrowgap, the maximum mesh size is 0.1 mm to resolve airflow through the gap of the height of 1.1 mm.
However, considering the probability of instability to trigger a whistling sound starting from the shear
layer, it is essential to calculate the boundary layer of the narrow -gap flow with sufficient grids for
successfully reproducing the whistling sound generation. The prismatic grids are distributed on thesurface of the side-mirror model to ensure that 𝑦 + is smaller than 1. The height of the first meshes,
the total height of prismatic meshes, and the number of prismatic layers were 0.01 mm, 0.1 mm, and6, respectively. The total numbers of grid cells and nodes were 29 million and 107 million, respectively.
The numerical methods described in this section are realized using the commercial software ANSYS
Fluent V19.1.

Figure 7 – Entire computational domain with related dimensions
Table 2 – Detailed values and options of boundary conditions of numerical domain.
Boundary

Type

Remarks

Inlet

Velocity inlet

22 m/s, non-reflecting condition

OutletPressure outlet

0 Pa (gauge), non-reflecting condition

Top, bottom, and sides

Pressure far-field

0 Pa (gauge), Ma = 0.0647

Figure 8 – Grids distributions (a) in the entire computational domain on a vertical plane passing sidemirror, (b) near guide-rib, (c) in the cavity, and (d) around the stopper in cavity.
4.2 Vortex Sound Source
Lighthill[10-11] derived the exact formula defining aerodynamic sound sources in a turbulent flowby transforming the set of continuity and Navier-Stokes equations into an inhomogeneous wave
equation. In this wave equation, the inhomogeneous term plays the role of a sound source:
𝜕 2 𝑇𝑖𝑗𝜕2( 2 − 𝑐0 2 ∇2 ) (𝜌 − 𝜌0 ) =,(4)𝜕𝑡𝜕𝑥𝑖 𝜕𝑥𝑗

where 𝑇𝑖𝑗 is Lighthill’s tensor:
𝑇𝑖𝑗 = 𝜌𝑣𝑖 𝑣𝑗 + ((𝑝 − 𝑝0 ) − 𝑐0 2 (𝜌 − 𝜌0 ))𝛿𝑖𝑗 + 𝜎𝑖𝑗 .
(5)With the conditions of inviscid flow, high Reynolds number, and adiabaticity, the aerodynamic
sound source is approximated by:𝜕 2 𝑇𝑖𝑗1~𝜌 𝑑𝑖𝑣(𝜔⃗ ×𝑢⃗ ) + 𝜌0 ∇2 ( 𝑢2 ).
𝜕𝑥𝑖 𝜕𝑥𝑗 0
2(6)Howe [12] reformulated Lighthill’s Equation using the total enthalpy B defined by:1
𝐵 ≡ ∫ 𝑑ℎ + 𝑣 2 ,2(7)

where the enthalpy h is given by:ℎ = 𝜌−1 𝑑𝑝 + 𝑇𝑑𝑆.
For homentropic flow with dS = 0, B is approximated by:
𝐵~

𝑝 1 2
+ 𝑣 ,
𝜌 2

(8)

(9)

which is considered the independent acoustic variable. For compressible, homentropic turbulent flow
with a low Mach number, Lighthill’s Equation is well approximated by:(1 ∂2− ∇2 ) B ~ 𝑑𝑖𝑣(𝜔
⃗ ×𝑢
⃗ ).
c02 ∂t 2(10)This means that the sound in terms of B is generated by the motion of the vortices. The righthandterm of Equation (10), 𝑑𝑖𝑣(𝜔⃗ ×𝑢⃗ ), is defined as the vortex sound source and used to identify themain sound source in this study.

5. NUMERICAL RESULTS
The boundary layer flow needs to be calculated with sufficient resolution for reliable internal flow
simulation through the narrow-gap. Figure 9a shows the predicted 𝑦 + distribution over the outersurface of the SSM. Figure 9b and 9c show that of the lower and upper surfaces of the narrow-gap of
the SSM. It can be seen that 𝑦 + is smaller than 1 for most surface areas. These results confirm that
the LES technique combined with the high-resolution meshes can resolve the internal and externalboundary layer flow satisfactorily.

Figure 9 –Distribution of 𝑦 + on (a) outer surface, (b) inner-under surface, and (c) inner-upper surface ofsimplified side-mirror model.
Figure 10 compares the sound pressure spectrum predicted at the same observer location as that of
the experiment with the corresponding measured spectrum, as shown in Figure 5. Although the whistlecomponent is observed at about 7500 Hz in the sound pressure spectrum measured for the SSM, thepredicted peak tonal component is located near 6000 Hz. The different whistle frequency between thetwo results seems to be due to the different inflow conditions. In the experiment, the inflow is driven
by the small wind tunnel with a nozzle outlet so that the inflow near the inlet of the SSM is not uniform,
whereas, in the numerical simulation, the inlet velocity on the entire inlet plane is prescribed , and thus
uniform inflow is incident on the SSM. These different inflow conditions seem to induce different
whistle frequencies. Also, the measured SPLs are much higher than the predicted ones in the entirefrequency range. As described in the experiment, the measured spectrum includes the noise due to themotor driving the fan and the jet flow of the nozzle of the small wind tunnel, thereby increasing themeasured SPL levels compared with the predicted one. For the same reason, the measured tonalcomponents due to the fan motor cannot be identified in the predicted spectrum.

Figure 10 – Comparison of sound pressure spectrum about SSM between prediction and experiment
Figure 11 shows the center gap plane, which is parallel to the narrow-gap's upper and lower
surfaces and passes the center of the narrow-gap height. Figure 12 shows the iso-contours of
instantaneous flow velocity and vorticity on the center gap plane. A typical vortex-shedding structure
can be found in the flow through the narrow-gap of SSM. Specifically, a lower flow velocity fieldforms near the inlet of the narrow-gap.
Figure 13 shows a fluctuating pressure field at the frequency of 6000Hz, obtained by conducting
the Fourier transform to the temporal pressure signal. The propagation of the whistling sound wave
can be clearly identified inside and outside the narrow-gap region. In addition, the incompressiblepressure fluctuations associated with the sound source can be found in the narrow-gap. This pressure
wave has much less wavelength than sound waves since the convection speed of the vortex is around
20 m/s while the sound speed is about 340 m/s.

Figure 11 – Center gap plane defined through the narrow-gap.

Figure 12 – Instantaneous external and internal flow isocontour on center gap plane in normal direction: (a)flow velocity and (b) vorticity.

Figure 13 – Fluctuating compressible and incompressible pressure fields at whistling frequency in center
gap plane
Figure 14 shows the distribution of the predicted velocity and vortex sound source defined in
Equation 10 in the center gap plane. As shown in Figure 14a, after the flow passes through the inletof the narrow-gap, the guide-rib blocks the inflow. Specifically, the strong edge flow forms at thelower edge of the guide-rib. Figure 14b reveals that the strong vortex sound sources are located alongwith the edge flow lines. These results imply that the instabilities of the shear layer starting from theedge of the guide-rib can be the primary source of the whistle sound.
For further analysis, the components of the vortex sound source at the whistling frequency of
6000Hz are extracted through the Fourier transform of the time-domain vortex sound source field.
Figure 15 shows the vortex sound source field at the whistling frequency, which reveals that the
primary source of the whistling frequency is generated by the trailing edge flow triggering the
instabilities of the shear layer.
For more direct evidence of whistle sound generation and propagation, the snapshots of fluctuatingpressure field at the whistling frequency are shown in Figure 16. It can be clearly seen that thecompressible sound pressure waves propagate from the edge of the guide-rib and originate from theedge-vortex flow. Note that the pressure wave with much less wavelength is the incompressible wave
associated with convecting vortices.

Figure 14 – Distribution of predicted flow velocity and vortex sound source in center gap plane: (a)velocity and (b) vortex sound source of SSM.

Figure 15 – vortex sound source field at whistling frequency in center gap plane of SSM.

Figure 16 – Fluctuating pressure field at whistling frequency in center gap plane of SSM at (a) beginning,(b) one-fourth, (c) two-fourth, and (d) three-fourth of whistling period.

6. NEW DESIGN FOR SUPPRESSION OF WHISTLE
In order to eliminate the whistle noise, the geometry of the guide-rib is modified by employing a
concept of a vortex generator which can destroy the observed strong coherent vortex. Figure 17 shows
the geometry of the proposed model, whose guide-rib is divided into five parts. This new one wasnamed the ‘Suppressed Whistle Model (SWM).’ Further numerical simulations and experiments arecarried out for the SWM.

Figure 17 – Geometry of suppressed whistle model: (a) virtual sample and (b) characteristic features.
Figure 18 shows the flow field predicted for the SWM. It can be seen that the trailing edge flow of
the guide-rib becomes so weak that there is no vortex source at the whistling frequency.

Figure 18 – Distributions of predicted flow field inside gap-flow region: (a) velocity, (b)vortex soundsource, and (c) vortex sound source at whistle frequency.
Figure 19 compares the experimental flow visualization results between the SSM and SWM using
a He-Ne LASER with oil smog. The strong coherent flow structures starting from the edge of theguide-rib are captured for the SSM, but those of SWM are relatively weak. Also, Note that the
distributions of highlighted oil smog were similar to those of numerical results for both models, which
confirms the validity of numerical simulations.

Figure 19 – Visualized flow structures using oil smog with He-Ne LASER: (a) SSM and (b) SWM.
Figure 20 compares the sound pressure spectrum predicted and measured for the SWM with thoseof the SSM. It can be found that the measured and predicted whistle components are successfully
eliminated in the SWM.

Figure 20 – Comparison of predicted and measured sound pressure spectrum between SWM and
SSM.

7. CONCLUSIONSThis study numerically and experimentally investigated the generation mechanism of whistle soundin a narrow-gap flow of a side-mirror using high-resolution LES techniques and a high-speed camera.
The flow noise measurement of the target side-mirror was conducted to characterize the whistlingsound at various flow velocities. It was found that the whistle sound began to occur at the flow velocity
of 18 m/s, and its frequency increased with the increasing flow velocity. Then, a series of flow noise
measurements were carried out by assessing the effects of complex geometry, such as holes and gaps
on the surfaces of the narrow-gap, thereby leading to the Simplified Side-mirror Model (SSM), which
was also manufactured using transparent material for the flow visualization experiment.
Three-dimensional unsteady compressible LES with high temporal and spatial resolutions was
carried out to clear out the generation mechanism of the whistle. The sound pressure spectrums
directly predicted at the monitoring point were compared with the measure one for the SSM, which
confirms the validity of the current numerical methods. In the narrow-gap region, it was identified
that the side edge of the guide-rib caused a high level of vortex sound source. Through the Fouriertransform, the vortex sound sources causing the incompressible and compressible pressure waves at
the whistling frequency were successfully visualized.
Finally, the Suppressed Whistle Model (SWM) was devised by employing the vortex generators
designed to destroy the observed coherent vortex structure and thus suppress the whistling sound.
Further numerical simulation showed that the SWM could eliminate whistle sound sources
successfully. To validate the suppression of whistling, the sound pressure spectrums due to the flow
passing through the SSM and SWM were experimentally compared. In addition, the flow visualization
with oil smog using He-Ne LASER and the high-speed camera was conducted about the SSM and
SWM. The flow structures of SSM were relatively strong than those of SWM, confirming that the
SWM was effective in suppressing the whistle sound.

REFERENCES
1. Chanaud, Robert C., “Aerodynamic Whistles”, Scientific American, vol. 222, no. 1, pp. 40–47, JSTOR.
(1970)
2. Lounsberry, T., Gleason, M., and Puskarz, M., "Laminar Flow Whistle on a Vehicle Side-mirror," SAE
Technical Paper 2007-01-1549. (2007)
3. Werner, M., Würz, W., and Krämer, E., "Experimental Investigations of Tonal Noise on a Vehicle Sidemirror." in: Dillmann, A., Heller, G., Krämer, E., Wagner, C., Breitsamter, C. (eds) New Results in
Numerical and Experimental Fluid Mechanics X. Notes on Numerical Fluid Mechanics andMultidisciplinary Design, vol 132. Springer, Cham. (2016)
4. Werner, M., Würz, W., and Krämer, E., "Experimental Investigation of Tonal Self-Noise Emission of a
Vehicle Side-mirror", vol. 55, no. 5, AIAA Journals. (2017)
5. Frank, Hannes M., Munz, Claus-Dieter, "Direct aeroacoustic simulation of acoustic feedback phenomena
on a side-view mirror", vol. 371, pp. 132-149, Journal of Sound and Vibration. (2016)
6. Pando, Miguel Fosas de, Schmid, Peter J., and Sipp, Denis, "A Global Analysis of Tonal Noise in Flows
Around Aerofoils, vol. 754, pp. 5-38, J. Fluid Mech. (2014)
7. Miyamoto, Masataka, Ito, Yasunori, and Takahash, Kin'ya, "Numerical Study on Sound Vibration of an
Air-reed Instrument with Compressible LES", arXiv preprint arXiv:1005.3413. (2010)
8. Velte, C. M., Hansen, M. O. L., George, W. K., and Meyer, K. E., "Characterization of Vortex Generator
Induced Flow", Technical University of Denmark, DCAMM Special Report. (2009)
9. Kwongi, Lee, Sonjune, Lee, Sangheon, Lee, and Cheolung, Cheong, "Numerical Investigation ofWhistling Sound in Narrow-gap Flow of Automobile Side-mirror", vol. 197, 108893, Applied Acoustics.
(2022)
10. Lighthill MJ., "On Sound Generated Aerodynamically. I. General Theory", vol. 211(1107), pp. 564-87,
Proc. Royal Soc. A: MathPhy.Eng. Sci. (1952)
11. Lighthill MJ., "On Sound Generated Aerodynamically. II. Turbulence as a source of sound", vol.
222(1148), pp. 1-32, Proc. Royal Soc. A: MathPhy.Eng. Sci. (1954)
12. Howe MS., "Contributions to the theory of aerodynamic sound with application to excess jet noise andthe theory of the flute", vol. 71(4), pp. 625, Proc. Royal Soc. A: MathPhy.Eng. Sci. (1975)

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022 in Gyeongju, Korea

ABS-0933

An aeroacoustics analysis on the effect of flexible trailing-edge
modifications at large chord-based Reynolds number
Rohit Singh and Akhilesh Mimani
1

Department of Mechanical Engineering, Indian Institute of Technology Kanpur
Kanpur 208016, Uttar Pradesh India

ABSTRACTThis paper presents an aeroacoustics investigation of a NACA0012 airfoil with different
modifications attached to the trailing-edge (TE) at a large Reynolds number. Experiments were conducted in
the large aerodynamic wind-tunnel facility where a two-dimensional airfoil of span L = 2.25 m and chord
length C = 0.75 m was tested for flow speeds ranging from 20 to 40 m/s which corresponds to a chord-based
Reynolds number ranging from 0.9 to 1.92 million, and angle-of-attack (AoA) from 0 to 10 degrees. The TE
modifications include an array of flexible (a) self-oscillating flaplets and (b) triangular serrations both having
a wetted area equal to 10% of chord length. For the case of flaplets, the acoustic spectra showed that at very
low frequencies, tones were observed due to self-oscillations resulting in a significant increase in noise levels
compared to the baseline while at mid-frequencies, about 3 to 4 dB noise reduction was observed, and a small
increase at high-frequencies. However, for the case of triangular serrations, only a minor reduction wasobserved in the low-to-middle frequency region while the levels slightly increase at high frequencies.
Keywords: Trailing-edge noise, Compliant serrations, Oscillating flaplets, Hard-wall wind-tunnel

1. INTRODUCTION
The interaction of boundary-layer (BL) with trailing-edge (TE) is the primary cause of airfoil selfnoise spectrum which typically comprises of two main components, namely, a broadband contribution andtonal noise peaks. The tonal noise is particularly annoying and usually occurs at a low-to-moderate Reynolds
number. Paterson et al. [1] presented one of the first investigations into airfoil tonal noise where they foundthat the primary tone peak can be scaled with the freestream velocity, U  by a factor of 0.8 within a limited
frequency range prior to jumping to a higher frequency, which is referred to as ‘laddering’. An empiricalmodel was developed based on a scaling relationship of U 1.5 after all of the laddering occurrences wereaveraged across a broad frequency range. To explain these findings, Tam et al. [2] suggested the generationof an aeroacoustic feedback loop that is self-excited, consisting of a noise source in the wake and instabilities
in the BL on the pressure side of the airfoil. Utilizing the theory of linear stability, Lowson et al. [3] andMcAlpine et al. [4] demonstrated that the tonal noise is controlled by the presence of a laminar separation
bubble on the pressure side of the airfoil and that its frequency is amplified in the BL. Desquesnes et al. [5]carried out a direct numerical simulation (DNS) on the tonal noise problem and discovered that a secondary
feedback loop was caused by airfoil suction side instabilities. The discrete frequencies that are uniformly
spaced around the primary tone were subsequently believed to have been modified by this feedback.
Given that airfoils are found in diverse engineering applications, efforts to reduce airfoil self-noise,
particularly by employing bio-inspired techniques or modifications have attracted significant researchinterest in recent years. Moreau et al. [6] presented an experimental study of the TE serrations on a flat-plate
at low-to-moderate Reynolds number 0.16 to 0.42 million and found that reductions of up to 13 dB in the
narrowband noise levels were achieved, and this is mainly due to attenuation of vortex shedding at the TE.
Geyer et al. [7] studied a variety of airfoils with various porosities, drawing inspiration from owls’ wellknown quiet flying and soft downy feathers. They observed a reduction of up to 10 dB in the low-to-mid
frequency region, although this depends on the porosity. Compared to a non-porous airfoil, there was anincrease in the high-frequency range which was attributed to the noise arising from surface roughness.
Additionally, compared to the non-porous airfoil, there was a penalty in aerodynamic performance as both
lift and drag forces were adversely affected. Jiang et al. [8] investigated the effect of porous-serrated
treatment at the TE of a NACA0012 airfoil at Reynolds number 0.19-0.32 million wherein it was found thatnoise reduction up to 16 dB could be achieved. Herr [9] and Finez et al. [10] investigated the TE brushes
which is a different bio-inspired approach that imitates the fringes seen on owl feathers. Herr noted a decreasein broadband noise produced by the turbulent BL interaction with the TE in the 1000 to 1600 Hz frequency
range, which ranged from 2–10 dB. Following this study, Finez et al. [10] demonstrated that the inclusion of
TE brushes reduces the spanwise coherence of the shed vortices by 25% and also indicated that a ratio of
coherence length to brush fiber diameter should be the criterion for future designs.
A study of the aeroacoustic performance of flexible (compliant) modifications to airfoil TE has also
received significant interest. Schlanderer and Sandberg [11] carried out a direct numerical simulation (DNS)
of an elastic TE where they observed an increase in noise at the eigenfrequency of the elastic material, andan aeroacoustic advantage, i.e., noticeable noise reduction at low and medium frequencies. Das et al. [12]experimentally investigated the noise reduction mechanism of an airfoil with a flexible TE at a low-tomoderate Reynolds number where they observed a noise reduction of 4 dB on average. Kamps et al. [13]presented an experimental study of the effect of silicone flaplets on the TE of an airfoil where they observed
a decrease in tonal noise but not in broadband noise component. By applying time-resolved particle image
velocimetry (PIV) on a NACA0012, Talboys and Brucker [14] demonstrated how an array of oscillating
flexible flaplets stabilized the angle of attack and the shear-layer at a moderate Reynolds number, and also
decreased the BL on the suction side of the airfoil resulting in a decrease in drag. Talboys et al. [15] studied
the effect of self-oscillating TE flaplets affixed to the pressure side on a NACA0012 airfoil at low-tomoderate Reynolds number 0.05-.35 million, and geometric angle of attack (AOA) from 0o-20o. It wasobserved that the flaplets could produce noise reduction of 1.5 to 2 dB in the low-frequency range, and theyargued that the mechanism responsible for noise attenuation is due to the breakdown of the vortices in the
TE wake in smaller eddies which was experimentally demonstrated by piezo-electric actuated oscillations of
the airfoil TE in Jodin et al. [16].
To date, there is no reported work that studies the aeroacoustic performance of compliant serrations

and self-oscillating flaplets attached to airfoil TE at high Reynolds numbers starting from nearly 1 million.
In light of the background provided, this paper presents an experimental investigation of the aeroacoustic
performance of an array of self-oscillating flexible flaplets and compliant triangular serrations attached to the
TE of a NACA0012 airfoil at high Reynolds number ranging from 0.9 to 1.9 million.

2. EXPERIMENTAL SETUPThis section presents the experimental set-up of a two-dimensional NACA0012 airfoil(schematically shown in Fig. 1(a)) in the National Wind Tunnel Facility (NWTF) which is a closed-circuitand closed-section (hard-wall) tunnel. The NWTF test section (see Fig. 1(b)) is 3.0 m wide, 2.25 m high, and8.75 m long. The length of 8.75 m is divided into two parts: an upstream part (5.75 meters) and a downstream(3 meters). A single-stage 12-bladed axial-flow fan driven by a 1000 kW variable speed DC motor can create
air speeds of up to 80 m/s in the test-section. The placement of four tiny mesh screens upstream of a 9:1
contraction and downstream of the honeycomb ensures a flow with extremely low turbulence intensity (TI)of less than 1%. For the experiments carried out in this work, two of the NWTF test section’s glass panels
were replaced with a thick piece of plywood in which holes were drilled to set up ¼” microphones at different
points which correspond to a modified Underbrink spiral design.
The NACA0012 airfoil test-case used in the study has a chord length C = 0.750 m and a span of L
= 2.25 meters. The model was made up of high-density foam (34-38 kg/m3) which was reinforced with a 3
mm thick metal sheet and reinforced with a rectangular pipe to strengthen the airfoil. The model was coatedwith a glass fiber layer for a high surface finish and TE bluntness was reduced to 1 mm, refer to thephotograph shown in Fig. 1(b). In order to fabricate the compliant triangular serrations and thin rectangularflaplets, a thin polyester film approximately 1 mm thick was considered, and it was cut into the desired shapes
using a laser-cut process. The width of the triangular serrations was taken equal to 75 mm (0.1 times thechord length), i.e., the tip-to-tip distance between the triangle vertices was equal to 75 mm (see Fig. 2(a)) andthe same depth was considered. For the rectangular flaplets, their length (depth) and width were taken equal
to 75 mm and 20 mm, respectively, while a gap of 3 mm was considered between two adjacent flaplets, seeFig. 2(b). Note that free-end of both triangular serrations and rectangular flaplets was located downstream at
1.1 times the chord length, and were allowed to self-oscillate in the flow field. Furthermore, in the case of anon-zero AoA, the flaplets were placed at the suction side of the airfoil.
The airfoil was placed at the center of the test-section at a 1.5 m distance from the wall and attachedto the turn table. Additionally, a pitot tube was located at upstream to measure the flow velocity as shown in
Fig. 1(b). Figure 3 shows a photograph of the test-cases; part (a) shows the baseline NACA0012 airfoil
without TE treatment, part (b) shows the airfoil model with self-oscillating flaplets while part (c) shows the
airfoil model with triangular serrations. In this work, flow velocity ranging from 20 m s up to 40 m s wasconsidered in steps of 5 m s which corresponds to a chord-based Reynolds number Re = 0.96 million to
1.92 million. Furthermore, the AoA ranged from 0 to 10 degrees in step of 2 degrees.

(a)

(b)

Figure 1 The photograph shows a NACA0012 airfoil (a) CAD drawing of airfoil and (b) experimental
arrangement in the test-section of the National Wind Tunnel Facility (NWTF) at IIT Kanpur.

(a)

(b)

Figure 2 A schematic diagram of (a) self-oscillating flaplets and (b) triangular serrations
The acoustic data was measured on a phased microphone array which consists of 32 ¼” GRAS 40 PH
microphones that were flush-mounted to a thick plywood frame that replaced the glass window. Note that theperpendicular distance of the spiral array plane to the airfoil mounting rod was equal to 1.5 m. The
microphones were connected to the 1073 NI PXIe chassis-mounted 4497 PXIe National Instruments (NI)data acquisition (DAQ) cards via BNC cables. LabView program is used to collect the microphone signals,
and it is connected to a PC with an i7 11th generation CPU and 32 GB of RAM. The microphone array and
DAQ system measured the noise data at a sampling frequency Fs = 65536 Hz for a sample time T = 15 s.
Blockwise fast Fourier transform (FFT) on Hanning-window blocks each of a size of 16384 samples and
50% overlap were used to convert the time-domain signals to the frequency-domain. Note that the data fromthe center microphone of the array (numbered 1) was considered for showing the airfoil spectra.

3. RESULTS AND DISCUSSION
Figures 4 to 8 show a comparison of the acoustic spectrum of the baseline NACA0012 airfoil modelwith the test-cases having TE treatments (self-oscillating flaplets and compliant triangular serrations) and thebackground noise spectrum for free-stream velocities U   {20, 25,30,35, 40} m  s 1 , respectively.

Foreach flow speed, parts (a-f) show the result pertaining to AoA   0, 2 , 4 ,6 ,8 and 10 , respectively.
Note that baseline NACA0012 airfoil and the models with TE treatments are untripped, i.e., the BL is allowed
to grow naturally near the leading-edge (LE) without artificially forcing it to transition to a fully turbulent
flow field.

Figure 3 The photograph shows a NACA0012 airfoil: (a) baseline test-case, (b) with self-oscillating flapletsand (c) with triangular self-oscillating serrations mounted in the test-section of the NWTF, IIT Kanpur.
Figure 4 shows that at relatively low flow speed U   20 m  s 1 (Reynolds number Re = 0.96
million), the acoustic spectrum of the baseline test-case and the models with TE treatments exhibit abroadband nature for all AoAs. In particular, note that the spectrum is nearly co-incident, and the TE
treatments can deliver only a small noise reduction (NR) roughly between 1 to 2 dB at certain AoAs as notedin Table 1.
Figure 5 shows that at flow speed U   25 m  s 1 (Reynolds number Re = 1.2 million), the acoustic
spectra are again nearly co-incident and exhibit a broadband nature up to   6. For larger AoA   8and 10 , the spectrum for airfoil model with self-oscillating flaplets exhibits multiple resonance peaks in the
low-frequency given by 64 Hz, 200 Hz and 328 Hz which is most likely attributed to the large amplitude
oscillations (instability) of the flaplets which behave like thin cantilever beams that are clamped at the TE
end of the airfoil and undergo forced oscillations in the flow field. Furthermore, at   8 , the flaplets
produce noise reduction between 2 to 4 dB in the mid-frequency range from 600 Hz to 1600 Hz but arecounter-productive at higher frequencies from 4000 Hz to 8000 Hz where they increase the self-noise by 3
to 6 dB. Therefore, from an overall point of view, the use of airfoil with flaplets at TE significantly increases
the overall sound pressure level (OASPL) for the reasons noted above. On the other hand, the spectra fortriangular serrations are found to be nearly co-incident with the broadband spectrum of the baseline case evenat high AoA.
Figures 6 and 7 show that at flow speeds U   30 m  s 1 and 35 m  s1 (Reynolds number Re = 1.44
million and 1.68 million, respectively), the spectrum for baseline test-case and the models with TE flaplets
are co-incident at   0. However, at AoA   2 onwards, the model with self-oscillating flaplets exhibits
multiple tones of diminishing magnitude at low frequencies while a noticeable reduction in airfoil self-noise
is observed in the mid-frequency range (refer to Table 1) which is followed by a small increase at highfrequencies. On the other hand, the spectra for model with triangular serrations are nearly co-incident withthe baseline test-case for both flow speeds.
Figure 8 shows that at the highest flow speed U   40 m  s 1 considered in this work (Reynolds
number 1.92 million), the spectrum for flaplets exhibits multiple resonance peaks even at zero AoA which
are also observed at higher AoAs. Note that at this speed, flaplets produce significantly less noise reductionin the mid-frequency range, refer to Table 1. Furthermore, as compared to the baseline test-case, the airfoil
model with triangular serrations also tends to generate more noise at higher frequencies for certain AoA.
Table 1 Reduction in noise and the frequency range of noise reduction in rectangular self-oscillating flaplets
Flow

Angle of attack

speed in degree

0o

2o

4o

1 to 2

1 to 23000 to 8000

3300 to

6o

8o

10o

(m/s)
Reduction (dB)20

Frequency range

-

(Hz)

1 to 2-

8000

Frequency range

2 to 4
-

-

-

-

(Hz)
Frequency range-

Reduction (dB)Frequency range

3.5 to 6

3.5 to 5.1

3 to 5

3.5 to 4.5500 to 3200

600 to 3000

600 to500 to500 to

3000

3000

2900

-

1 to 2

2 to 3.5

3 to 4.2

2 to 2.7

2 to 4.2

800 to1800

700 to 2200

600 to640 to

600 -

3100

2700

3000

(Hz)
Reduction (dB)40

Frequency range(Hz)-

3.5 to 4.5

(Hz)
35

600 to1600

Reduction (dB)302000 to8000

Reduction (dB)
25

-

-

2 to 4

1 to 21400 to 2000

1000 to1700

1 to 2.5--700 to1300

Figure 4 Acoustic spectra of the NACA0012 airfoil: Comparison of the results for baseline test-case withairfoil models having TE treatments at flow velocity 20 m/s and AoA (a) 0o, (b) 2o, (c) 4o, (d) 6o , (e) 8o and(f) 10o .

Figure 5 Acoustic spectra of the NACA0012 airfoil: Comparison of the results for baseline test-case withairfoil models having TE treatments at flow velocity 25 m/s and AoA (a) 0o, (b) 2o, (c) 4o, (d) 6o , (e) 8o and(f) 10o .

Figure 6 Acoustic spectra of the NACA0012 airfoil: Comparison of the results for baseline test-case withairfoil models having TE treatments at flow velocity 30 m/s and AoA (a) 0o, (b) 2o, (c) 4o, (d) 6o , (e) 8o and(f) 10o .

Figure 7 Acoustic spectra of the NACA0012 airfoil: Comparison of the results for baseline test-case withairfoil models having TE treatments at flow velocity 35 m/s and AoA (a) 0o, (b) 2o, (c) 4o, (d) 6o , (e) 8o and(f) 10o .

Figure 8 Acoustic spectra of the NACA0012 airfoil: Comparison of the results for baseline test-case withairfoil models having TE treatments at flow velocity 40 m/s and AoA (a) 0o, (b) 2o, (c) 4o, (d) 6o , (e) 8o and(f) 10o .

4. CONCLUSION
This paper has presented an experimental investigation of the effect of flexible trailing-edge (TE)modifications attached to the suction side of a NACA0012 test-model on the airfoil self-noise reduction atlarge Reynolds number ranging from 0.96 to 1.92 million, and geometric AoA ranging from 0 to 10 degrees.
The flexible TE modifications studied in this paper include self-oscillating flaplets and triangular serrations.
Experiments were carried out in the National Wind Tunnel Facility (NWTF), IIT Kanpur on the baseline testcase of a two-dimensional NACA0012 airfoil model of span L = 2.25 m and chord length C = 0.75 m which
exhibited a broadband spectrum at different flow speeds and AoAs due to the completely turbulent nature of
the BL near the TE. For the case of NACA0012 model with self-oscillating TE flaplets, a broadband spectrum
was observed at low flow speeds and small AoAs which was nearly co-incident with the baseline test-case.
However, at higher flow speeds and larger AoA, the spectrum of self-oscillating flaplets exhibited multiple
resonance peaks in the low frequency range which is most likely attributed to large amplitude oscillations
that is possibly generated by a strong interaction with the wake vortices. In the mid-frequency range from500 to 3200 Hz, a small noise reduction of 2 to 4.5 dB was observed while at high frequency, marginallymore noise was generated. From an overall point of view, the use of self-oscillating flaplets appears to be
counterproductive at large Reynolds number as the overall sound pressure level (OASPL) increases
considerably due to the low frequency resonances – an effect observed for the first time. On the other hand,the acoustic spectrum of the compliant triangular serrations exhibited a broadband nature for the entire range
of Reynolds number and AoA considered in this study. In fact, at such large Reynolds number, the flexible
triangular serrations were not found to be very effective in controlling TE noise emissions.
Future investigations will focus upon the investigating the effect of different types of flexible TEserrations and flaplets on the aeroacoustic noise emitted as well as the aerodynamic performance of threedimensional, i.e., wall-mounted airfoils at large Reynolds numbers. Furthermore, work is underway todevelop beamforming algorithms which can simultaneously reduce the high levels of background noise andalso de-reverberate the microphone signals obtained in the hard-wall tunnel to produce high-quality image
source maps which shows the spatial location of airfoil self-noise sources.

Acknowledgement
This work was funded by the Science Education and Research Board (SERB) New Delhi, INDIA throughits Start-up Research Grant SRG/2019/000885 ‘Resolving airfoil self-noise mechanism using diagnostic
acoustic imaging tool’ – the authors gratefully acknowledge the financial support. The authors would
also like to thank the NWTF technicians Mr. Tanu Shukla and Mr. Heerendra Kumar and the researchestablishment officer Mr. Sharad Saxena, for their help in conducting the experiment.

REFERENCES
1. Paterson RW, Vogt PG, Finkt MR, Munch CL. Vortex Noise of Isolated Airfoils. Journal ofaircraft. 10(5).
2. Tam CKW. Discrete tones of isolated airfoils. The Journal of the Acoustical Society ofAmerica 55(6):1173–1177.
3. Lowson M, Fiddes S, Nash E. Laminar boundary layer aero-acoustic instabilities. In: 32nd
Aerospace Science Meet and Exhibit, American Institute of Aeronautics and Astronautics, Reston.
4. McAlpine A, Nash E, Lowson M (1999). On the Generation of Discrete Frequency Tones by the
Flow around an Aerofoil. Journal of sound and vibration 222(5):753–779.
5. Desquesnes G, Terracol M, Sagaut P. Numerical investigation of the tone noise mechanism overlaminar airfoils. Journal of Fluid Mechanics 591:155–182.
6. Moreau D, and Doolan C. Noise-Reduction Mechanism of a Flat-Plate Serrated Trailing Edge.
American Institute of Aeronautics and Astronautics journal, Vol. 51, No. 10.
7. Geyer TF, Sarradj E, Fritzsche C. Measurement of the noise generation at the trailing edge ofporous airfoils. Experiments in Fluids volume 48, pages291–308 (2010).
8. Jiang C, Fischer J, Moreau D and Doolan C. Experimental Investigations of Novel Porous-Serrated
Treatments on Airfoil Trailing Edge Noise Reduction. 25th AIAA/CEAS Aeroacoustics
Conference, 20-23 may 2019.
9. Herr M. Design Criteria for Low-Noise Trailing-Edges. 13th AIAA/CEAS Aeroacoustics
Conference (28th AIAA Aeroacoustics Conference).
10. Finez A, Jondeau E, Roger M, Jacob MC. Broadband noise reduction with trailing edge brushes.
16th AIAA/CEAS Aeroacoustics Conference.
11. Schlanderer SC, Sandberg RD. DNS of a Compliant Trailing-Edge Flow. In: 19th AIAA/CEAS
Aeroacoustics conference., American Institute of Aeronautics and Astronautics 1–18.

12. Das C, Mimani A, Porteous R, Doolan C (2015) An experimental investigation of flow-induced
noise mechanism of a flexible flat-plate trailing-edge. Annual Conference of the Australian
Acoustical Society) 5(1):1–10.
13. Kamps L, Br¨ucker C, Geyer TF, Sarradj E. Airfoil Self Noise Reduction at Low Reynolds
Numbers Using a Passive Flexible Trailing Edge. In: 23rd AIAA/CEAS Aeroacoustics Conf.,
American Institute of Aeronautics and Astronautics.
14. Talboys E, Br¨ucker C. Upstream shear-layer stabilisation via self-oscillating trailing edge flaplets.
Experiments in Fluids (2018) 59:145.
15. Talboys E, Geyer T, and Br¨ucker C. An aeroacoustic investigation into the effect of selfoscillating trailing edge flaplets. Journal of Fluids and Structures, Volume 91, November 2019,102598.
16. Jodin G, Motta V, Scheller J, Duhayon E, D¨oll C, Rouchon JF, Braza M. Dynamics of a hybridmorphing wing with active open loop vibrating trailing edge by time-resolved PIV and force
measures. Journal of fluids and structures 74:263–290.

ABS-0167

Acoustic radiation from a finite length duct
Ben Baddour(1) , Philip Joseph(2) , Alan McAlpine(3) ,Ronnie Leung(4)(1) University of Southampton, England, b.baddour@soton.ac.uk(2) University of Southampton, England, pfj@isvr.soton.ac.uk(3) University of Southampton, England, am@isvr.soton.ac.uk(4) University of Southampton, England, R.E.Leung@soton.ac.uk

ABSTRACTThis paper presents an approximate model for the acoustic radiation from a finite length duct. This work is
motivated by a need to better understand the radiation from marine propellers and aerospace rotors, which areoften ducted to enhance their efficiency. The model allows for a better understanding of the radiated noise fromducted sources which, in turn, may be used to reduce the radiated noise by for example using duct liners. The
model is used to explore the effects of duct length on the radiated noise, and the effect of source location relative
to the open end. Predictions from the model will be compared against radiation from sources in free-fields toestablish when the effect of the duct may be neglected in noise predictions. The model will also be used to
explore the differences in radiation between the forward and rear-arcs.

Keywords: Duct, Acoustics, Modes, Modal, Radiation

1

INTRODUCTION

In this paper we not only derive a model for the acoustic radiation from a finite length duct, but this model
is compared to equivalent open radiation models, identifying the effect of a duct on free-field sources. The
finite length duct model is inclusive of ducts with negligible and small lengths where propagating and nonpropagating, cut-off, modes have the potential to radiate efficiently.
In this paper we base our study on work completed by Hewlett, Nelson and Morfey [1], who formed an
approximate solution for the radiation from a finite length duct, terminated at both open ends with an infinite
flange Using a semi-infinite pressure radiation model and accounting for reflection at both open ends, they wereable to predict the far-field radiation from a point monopole source in a finite length duct.
In this paper we expand and generalise the work of Hewlett, Nelson and Morfey [1], using the un-flanged duct
model of Gabbard and Astley [2] which is based on the earlier classical work of Homich and Lordi [3]. Ourmodel is not restricted to a point monopole and is general to any ideal source model readily incorporated into
a duct, such as dipole sources.
In this paper we consider a rotating point dipole source inside a finite length duct, starting from the model of
Baddour et al [4], who investigated a semi-infinite duct. In their paper, Baddour et al investigated the effect ofsource axial and radial location on the radiated mean square pressure from a semi-infinite duct. They found thatsources located at the open end of the duct give equal open and ducted radiation. Furthermore sources near thewall of the duct largely increase the pressure radiation from inside the duct, which is caused by cut-off mode
radiation.

2

RADIATION OF ROTATING FREE-FIELD POINT DIPOLE SOURCES AND THOSESHROUDED INSIDE A FINITE DUCTIn this section we summarise the free-field radiation of rotating point dipole sources and present a modification
to the semi-infinite duct radiation model presented by Baddour et al [4].
As sketched in figure 1 in both the free-field and ducted cases an unsteady point force at a single frequency ω,F (ω) is assumed to rotate at angular velocity Ω around the z axis with radius of rotation r p . The point dipole
source is assumed to be orientated at angle γ in the z − θ plane. Far-field observers are indicated in a sphericalcoordinate system at position (R, φ , θ ) centred on a point located at an axial distance z p from the centre ofrotation (x, y, z) = (0, 0, 0), where R is the radial distance and θ and φ are the azimuthal and polar angles
respectively. In figure 1b the rotating dipole source is assumed to be located within a hard walled circular ductof length L, radius a and cross sectional area S.

(a) Open source(b) Ducted source

Figure 1. Coordinate system of open and ducted sources
Following Baddour et al [4] the mean square radiated pressure from free-field open rotating point dipole sources
is a modal solution, where each azimuthal mode m radiates of the form,

p2

(O)


(R, φ , ω) =

1
4πR

2

∞

∑

m=−∞



m
sin γ + k cos φ cos γrp2

F 2 (ω − mΩ)Jm2 (kr p sin φ ),(1)

where F 2 (ω − mΩ) is the mean square fluctuating force and k is the acoustic wavenumber, which for medium
speed of sound c0 is calculated ω/c0 . The total pressure field is hence predicted using
p2

(O)

∞

(R, φ , ω) =(O)

∑ p2 m (R, φ , ω).

(2)

m=−∞

We now present an approximate model for the far-field radiation from a duct of finite length, using the semiinfinite duct model of [2] and [4]. The finite length duct model is based on the work of Hewlett, Nelson and
Morfey [1]. Unlike Hewlett, Nelson and Morfey our model does not restrict the analysis to a point monopole,and is valid for any source model that can be described with a source weighting aS,mn (ω).
We start with an analysis of the modal weighting at the source plane, for radial and azimuthal modes m and n,which for a point rotating dipole source with initial location (r p , θ̃ p , z p ) was shown by Baddour et al [4] to beof the form,
aS,mn (ω − mΩ) =
1 am sin γ + kz,mn a cos γ F(ω − mΩ)
2S r pk

Jm (κmn r p ) jmθ̃ p
1
q
e
,
m2
Jm (κmn a)z,mn a 1 − (κ a)2mn(3)

where κmn is the radial wavenumber, calculated by applying the hard-walled boundary condition to the Helmholtz
equation, and kz,mn is the axial wavenumber. The acoustic, radial and axial wavenumber are related by the dispersion relationship.
To compute the radiated acoustic field, the modal weighting amn (ω) at the duct open ends is required. Consider
the modal weighting apparent from a sum of four classes of waves discussed in Hewlett [1],1. The right going wave,
2. The reflected waves as a consequence of the incident right going wave, and further reflected waves originating from the right going wave, which reflect every propagation of duct length L.
3. The left going wave.
4. The reflected wave as a consequence the incident left going wave and further reflected waves originatingfrom the left going wave, which reflect every propagation of duct length L.
Each mode reaching the open end causes scattering into all radial modes of the same azimuthal order m. This
gives rise to the matrix formulation of the modal weighting at the open end, where the modal weighting of allmodes of the same azimuthal order m are dependent on each other and hence must be considered simultaneously. Introduce the matrix equation of modal weightings,(r)(l)
a m (ω) = P m (z)aaS,m (ω) + P m (z)bbS,m (ω) ,(4)

where the modal weightings a S,m (ω) and b S,m (ω), are column vectors of the right and left going modal weightings at the source plane respectively, each defined as

aS,m1 (ω)









 aS,m2 (ω) ,a S,m (ω) = 
..



.


aS,mn′ (ω)

bS,m1 (ω)







 bS,m2 (ω) b S,m (ω) = 
..



.


bS,mn′ (ω) ,(5)

truncated at n = n′ , in principal this vector continues to infinity n′ → ∞. For a semi-infinite duct the modal
weighting at the open end is solely dependent on the right going wave, however the finite length duct requiresconsideration of the both the left and right going waves.
(r)
Returning to Eq. 5, P m (z) is the sum of s propagation factors from the incident and each reflected wave,(r)apparent at the right open of the duct as a consequence of the incident right going wave. The term P m (z) isdefined∞(r)(r)
P m (z) = ∑ E m,s (z) ,

(6)

s=0

(r)

where each term of the series E m,s (z) is the propagation of the cumulative distance z traveled by the reflected
or incident wave reaching the right open end the sth time, using the propagation factor
e jkz,m1 z .
E m (z) =  ..

0

...

0

e jkz,m2 z
e jkz,mn′ z




.


(7)

(l)

The sum of the propagation factors, p m (z), from the incident and each reflected wave, apparent at the right
open of the duct as a consequence of left going incident wave, is similarly defined.
(r)(l)
The terms P m (z) and P m (z) are now obtained by analysing the cumulative distance traveled by each wave
component. Consider a right going wave released from a rotating point source, as shown in figure 2, whichhighlights that the cumulative distance traveled, z for this term is z = z p .

Figure 2. right going wave, s = 0 termPart of the mode will radiate and will contribute to the total modal weighting at the right end of the duct of
the form(r)
E m,s=0 (z) = E m (z p ) ,(8)which is the zeroth term of an infinite series of s waves that contribute to the modal weighting at the open end.
The mode will then reflect and scatter into other modes. The mode at the right open end reflects, governed byr m (ka) discussed in Gabbard and Astley [2], and propagates back into the duct. The mode then reaches the left
open end, reflects once more before once again reaching the right open end and contributing to the cumulative
modal weighting.
The propagation of the the s1 term is shown in figure 3, which highlights that the cumulative distance traveled,z for this term is z = z p + 2L

Figure 3. right going wave, s = 1 term
The next contribution to the infinite series of waves is of the form(r)
E m (z p + 2L) .
E m,s=1 (z) = r 2m (ka)E(9)

Combining the first 2 terms of Eq. 8 and Eq. 9 respectively and noting the relation between them, reveals themodal weighting is a sum of s terms of the form,∞(r)
E m (z p + 2sL) ,P m (z) = ∑ r 2sm (ka)E
s=0

which can be solved using simple geometric progression to show,

(10)


(r)
E m (2L)] .
P m (z) = E m (z p )Inv [II − r 2m (ka)E(11)

where Inv denotes a matrix inverse. Similar analysis is repeated for the left going wave, noting the initial
distance between the source and left open end is L − z p , consequently the mode propagates a total distance
2L − z p before reaching the right open end. The s = 0 term of the left going incident wave of modal weighting
b at the right open end is of the form(l)
E m (2L − z p ) .
E m,s=0 (z) = r m (ka)E(12)

Each subsequent propagation and reflection is of the same form as for the right going wave denoted by thedifference between the zeroth and first term of the summation in Eq. 6 denoted by Eq. 8 and 9. The left goingwave summation of propagation factors is of the form∞(l)
E m (2L − z p + 2sL) ,P m (z) = ∑ r 2s+1
(ka)E
m

(13)

s=0

which can be solved using simple geometric progression to show,(l)E m (2L − z p )Inv [II − r 2m (ka)E
E m (2L)] .
P m (z) = r m (ka)E(14)

For simplicity it is assumed the source radiates equally in both directions hencea S,m (ω) = b S,m (ω) .

(15)

Substituting Eq. 11, Eq. 14 and Eq. 15 into Eq. 4 leads to,a m (ω) = R m (Z (r) , Z (l) , ka)aaS,m (ω) ,(16)

where Z (r) and Z (l) are the distances the direct (incident) left and right wave travel before reaching the right
open end, which for the right going wave is z p and 2L − z p respectively. In Eq.16 R m (Z (l) , Z (r) , ka) is of theformE m (Z (r) ) + r m (ka)E
E m (Z (l) )]Inv [II − r 2m (ka)E
E m (2L)] ,R m (Z (r) , Z (l) , ka) = [E(17)which can be substituted into the matrix form of the far-field pressure radiation, forming the sum of the radiatedpressure of a single azimuthal order m for all radial n orders. The approximate far-field radiated acousticpressure from a finite length duct is of the form(D)
Rm (z p , 2L − z p , ka) + D Tm (π − φ , ka)R
Rm (L + z p , L − z p , ka)
pm (R, φ , θ , ω) ≈ D Tm (φ , ka)Ra
e− j(kR+mθ ) ,a S,m (ω)R

(18)

where D Tm (φ , ka) and D Tm (π − φ , ka) are row vectors of directivity factors at a single far-field angle φ . The
mean square pressure can be predicted using,p2(D)(R, φ ) =

2
1 ∞
(D)
pm (R, φ , θ ) .
∑2 m=−∞(19)

3

COMPARISON BETWEEN FREE-FIELD AND DUCTED RADIATIONThis section presents predictions for the multi-modal far-field mean square pressure fields from rotating point
dipole sources open in a free-field and inside ducts of finite length. The purpose of this investigation is toanalyse how altering physical parameters, such as source location and duct length, affects the far-field meansquare pressure radiation.
3.1 Effect of duct length on the far-field direcitivty of free-field open and ducted sources
This section compares the mean square pressure p2 (R, φ , ω) radiated from free-field open rotation point dipole
sources, and those shrouded inside a duct of finite length.
A duct length of L/λ ≈ 0.0, L/λ = 5 and 10 is now investigated in figure 4. The mean square pressure
p2 (R, φ , ω) is simulated at the representative low and high non-dimensional frequencies ka = 5 and 35. The
axial source location is simulated in the center of the duct. In each case only the forward-arc is shown, as the
directivity is symmetric about φ = 90◦ as z p = L/2. The simulations are conducted for far-field distance andsource strength of unity and a dipole orientation of γ = 0◦ .

(a) ka = 5(b) ka = 35

Figure 4. Mean square pressure for free-field rotating point dipole sources, and those inside a finite length ductof various lengths, located in the centre of the duct z p = L/2 and open in a free-field. The radius of rotationand dipole orientation are simulated to be r p /a = 0.5 and γ = 0◦ respectively. Plotted in decibels.
The effect of the duct length is seen to significantly affect the directivity for the relatively low frequency caseof ka = 5, Figure 4a shows the directivity varies by up to 4 dB. However, for the higher frequency case, shownas ka = 35, the effect of duct length is very small, which figure 4b shows is less than 2 dB and mostly limited
to the sideline directions φ ≈ 90◦ .
For the case of the duct of negligible length L/λ ≈ 0, the source is located at both open ends. Similar behavior
is observed here as was seen in Baddour et al [4] where the open and ducted field equate for a large rangeof the forward-arc, which for the finite duct case is seen to be represented by almost the entire arc, except asmall region in the sideline directions φ ≈ 90◦ . In principal a duct length of L/λ ≈ 0 would have no effect on
the radiated mean square pressure, as effectively the duct is ’non-existent.’ This is not observed in any of thesimulations presented in figure 4. This identifies the limitations of the model.
3.2 Effect of source axial location on the far-field direcitivty of free-field open and ducted sources
Now consider the effect on the mean square pressure p2 (R, φ , ω) by altering the source location z p . Figure
5 shows the mean square pressure p2 (R, φ , ω) for a duct length L/λ = 5 and three axial source locationsz p /λ = 2.5, 1 and z p /λ ≈ 0 for rotating point dipole sources using the same parameters as those used in figure4.

(a) ka = 5(b) ka = 35

Figure 5. Mean square pressure for a free-field open rotating point dipole sources with a radius of rotation ofr p /a = 0.5 and those shrouded inside a duct of length L/λ = 5 at various axial locations z0 . Plotted in decibels.
The source at the right open end, z p /λ ≈ 0 shows the open free-field and ducted pressure fields equate for alarge range of the forward-arc. Furthermore at the higher frequency investigated ka = 35, for sources not at the
open end z p /λ > 0, small oscillations are observed in the ducted radiation which is generally shown to have an
average value of approximately the open radiation. However, the source axial location at the higher frequency
investigated, ka = 35 is shown to have a relatively small effect on the radiated pressure field. This is identicalbehavior to that discussed in Baddour et al [4], for the semi-infinite duct.
3.3 Effect of radius of rotation on the mean square pressure radiated from free-field open and ducted sources
This section investigates the radius of rotation on the open and ducted radiated mean square pressure fields for.
Analysis is conducted for a short duct, L/λ = 0.1, where cut-on and cut-off modes have the potential to radiate
efficiently. Figure 6 shows the mean square pressure p2 (R, φ , ω) of a free-field open rotating point dipole source
and those shrouded by a duct of length L/λ = 0.1, for three radii of rotation r p /a = 0.0 (not rotating) 0.5 and
1.0, using the same parameters as those used in figure 4.

(a) ka = 5(b) ka = 35

Figure 6. Mean square pressure for a rotating point dipole sources at the center, z p = L/2 of a duct of length
L/λ = 0.1 and in a free-field for radii of rotation r p /a = 0, 0.5 and 1. Plotted in decibels.
Perhaps most striking in figure 6 is where the source is located near the wall of the duct r p /a = 1.0. Due tocut-off mode radiation the duct is shown to amplify the mean square pressure considerably. This effect is mostnotable in the sideline directions, where the free-field open pressure has no radiation but the ducted radiation
is fairly equal at all angles (similar to monopole radiation). The other two radii of rotation investigated r p /a =0.0 and 0.5 are shown to give a very similar radiated field, which at the higher non-dimensional frequency
investigated ka = 35, are indistinguishable, except at the sideline directions φ ≈ 90◦ .

3.4 Numerical validation using COMSOL Multiphysics
This section details numerical simulations conducted using COMSOL Multiphysics predicting the far-field radiation from point dipole sources on the axis r p /a = 0.0 of a finite length duct. The purpose of these simulations
is to validate the theoretical results presented in the previous sections.
Figure 7 shows a comparison between the mean square pressure (normalised) for a point source on axis r p /a =0, calculated using the theoretical model and using COMSOL Multiphysics. Comparisons are made for ka =5, 10 and 35, and a duct length L = 5λ for the source at the center z p = L/2.

(a) Dipole ka = 5(b) Dipole ka = 10(c) Dipole ka = 35

Figure 7. Mean square pressure computed using COMSOL Multiphysics (red dashed line) and the theoreticalmodel (solid black line) for a point dipole on the axis r p = 0 at the center z p = L/2 of a duct of length L = 5λ .
The non-dimensional frequency ka is shown to largely vary the agreement between the two models. Bestagreement is observed for the ka = 35 case, figure 7c, considering the point dipole, agreement is observed towithin 2 dB. Good agreement is observed for the ka = 10 case, figure 7b, except near φ = 90◦ where COMSOLMultiphysics predicts a stronger null. However, the two models predict a very different directivity for the low
frequency ka = 5 case, figure 7a, implying the model is limitted to the higher frequencies.

4

CONCLUSION

In this paper we have derived a theoretical model for the acoustic radiation from a duct of finite length. We
have compared this model to an equivalent free-field open source to identify the effect of the duct. The duct
length and axial location have been investigated to find they have a small effect at high frequency, and the radiusof rotation has been investigated to find large increase in ducted radiation is observed for sources rotating close
to the wall of the duct. The behavior is believed to be a result of cut-off mode radiation.

REFERENCES
5[1] Hewlett DAK, Nelson P, Morfey C. The radiation from acoustic sources within a finite length circular duct
immersed in water. Proceedings of a meeting - Internoise, 1997.
[2] Gabard, G and Astley, RJ. Theoretical model for sound radiation from annular jet pipes: far-and near-field
solutions. Journal of Fluid Mechanics, volume 549, 2006 pg 315–341.
[3] Homicz, GF and Lordi, JA. A note on the radiative directivity patterns of duct acoustic modes. Journal ofSound and Vibration, volume 41, 1975 pg 283–290.
[4] Baddour B, Joseph P, McAlpine A, Leung R. Open-to-Ducted Transfer Function for Point Dipole Sources.
28th AIAA/CEAS Aeroacoustics 2022 Conference, 2022, 3083.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022, in Gyeongju, Korea
Extended abstractABS-0261

Characterization of acoustic pressure radiation from compressordischarging piping system due to internal refrigerant flow in
outdoor air-conditioner unit
Sangheon LEE1; Cheolung CHEONG1; Jinhyung PARK2; Jangwoo LEE2
1

Department of Mechanical Engineering, Pusan National Univiersity, Republic of Korea
2

LG electronics, Republic of Korea

ABSTRACT
Among the components constituting the outdoor air-conditioner units, compressor piping systems are thecritical parts that determine its noise performance. For high efficiency, as the compressor operating speed
increases, the flow-induced vibration of the piping system, rather than structural-borne vibration, becomesthe main contributor to the external noise radiation from the compressor piping system. The flow-induced
pipe vibration and noise radiation from the pipe vibration involve complex physical mechanisms. This study
develops an efficient numerical methodology for predicting acoustic pressure radiation from a compressordischarging piping system due to internal refrigerant flow. The flow-borne noise of the piping system ischaracterized in association with inflow disturbance and vibrational modes of the relevant parts constituting
the piping system. Firstly, the internal refrigerant flow of the compressor-discharging piping system in theoutdoor air-conditioner unit was predicted by numerically solving the Navier-Stokes equations with Large
Eddy Simulation (LES) techniques. Then, the finite-element/boundary-element (FE/BE) coupled method isused to predict the dynamic response of the piping system and its radiated noise. In this step, the flow pressure
on the inner wall of the piping system, which was obtained from the LES result, was used as an input for thevibration analysis. There was good agreement between the predicted and measured results.
Keywords: Flow noise, flow-induced pipe vibration, flow-structure interaction, flow-vibroacoustic coupling,
compressor piping system, air-conditioner piping noise

1. INTRODUCTION
In a air-conditioner system, the compressor in the its outdoor unit is the core component that
determines the cooling or heating performance. For high performance and efficiency, the operating
speed of compressor tends to increased. This cause the increment of flow velocity of refrigerant in thepiping system connected to the compressor. It is well known that the flow born noise is proportional
to six -order of higher of flow velocity, while the structure born noise is proportional to the secondorder of flow velocity. Therefore, the high velocity refrigerant flow raises the relative contribution to
the noise compared to the compressor vibrational noise.
There are many research related to the flow induced noise in pipe. Zhang et al. [1] investigated theflow-born noise in curved pipe. They evaluated the vorticity disturbance as the criteria for the aeroborn noise and employed the middle plated to reduce the noise. However, the vibrational characteristicof the pipe was not included in the noise analysis step and there are large error from experimental
results. Ku et al. [3] decomposed the pressure fluctuation field of the critical nozzle flow into theincompressible and compressible ones by using the wavenumber-frequency transform and showed thatthe compressible pressure field made more contribution in a high -frequency range. However, this1

tkdwjdwjd222@pusan.ac.kr; ccheong@pusan.ac.kr

2

jh0311.park@lge.com; jonathan.lee@lge.com

study did not associate the identified incompressible and compressible pressure fields with the vibro acoustical feature of the relevant structure system. Timm et al.[3] developed the numericalmethodology for predicting the flow induced noise for water pump. They computed the turbulent flow
generated by the centrifugal fan in the pump. The results had a good agreement with the experiment’s
ones. However, they said, the pipe connected to the pump had to be included as the transfer path of
the noise to reduce the error. The piping system is the important noise source for the appliance thathas the flow device. The flow induced vibration and noise in the piping system has complicate physicalmechanism. Therefore, to accurately predict the noise radiation in the air-conditioner outdoor unit,
the reliable numerical methodology considering the physical mechanism is needed. In this paper, todevelop the numerical methodology for predicting flow induced vibration and noise in the piping line
three sequential numerical analysis was conducted. First, the turbulent flow in the piping system incomputed. Second, the dynamic response of pipe is computed using Finite Element (FE) method. In
this step, the static pressure generated by turbulent flow is applied to the pipe wall as an input load.
Finally, the acoustic analysis was conducted by using Finite Element (FE) and Boundary Element (BE)method. The velocity response of the pipe was used as an input sound source. The validity of numericalmethodology was confirmed by comparing the numerical results with the measured ones.

2. Numerical method
2.1 Computation Fluid Dynamics (CFD)
The turbulent flow in the piping system of compressor was predicted by solving Navier-Stoked
equation with Large Eddy Simulation (LES). In this step, the Smagorinski-Lilly model was adopted
as the subgrid scale model. Refrigerant-410A(R410A) was employed as the working fluid. Since thestated of R410A was set to high pressure and temperature vapor, the Aungier-Redlich-Kwong model
was used as the real gas model. The pressure-velocity coupling and spartial discretization scheme isshown in Table 1. The static pressure is extracted for the vibrational analysis.
Table 1: Solution method setting
Setting

Value

Pressure-velocity coupling

Simple C

Pressure discretization

2nd order upwind

Momentum discretization

2nd order upwind

Energy discretization

2nd order upwind

2.2 Vibrational and acoustic analysis
The vibrational analysis was conducted at the time domain by using Modal Superposition method.
The Static pressure obtained from the CFD analysis was interpolated to the FE mesh and used as apressure load. The fixed boundary condition was applied considering the compressor and pipegeometry. The near-field and far-field noise was computed by using FE mesh and BE meshrespectively. The velocity response of pipe external wall was used as an acoustic source. Since theacoustic analysis was conducted in the frequency domain, the velocity response of pipe external wall
was converted from time domain to frequency domain using Fourier Transform. At the boundary the
non-reflection boundary condition called Automatically Matched Layer (AML) was applied.

3. Results
The CFD results showed that there were two components that cause significant vorticity
disturbance. The one was muffler and the other was four-way valve. These noise sources were affectedby the pressure pulsation created at the compressor discharge pipe. The comparison results between
numerical and measured results confirmed the validity of the developed numerical methodology. Bythis research, it is expected that the numerical methodology can be used as the effective design tool
to reduce low noise air-conditioner outdoor unit at the development stage.

REFERENCES
1. Zhang C., Luo Y., Liang J., Li L. and Li J. Flow-induced noise prediction for 90° bend pipe by LES and
FW-H hybrid method, Scientific Research and Essays, 2014; 9(11):483-494.
2. Timm H., Thomas L. and Gunther B. A combined CFD-FEM approach to predict fluid-borne vibrationand noise radiation of a rotary vane pump. Energies 2021; 14:1874-1896.
3. Ku G., Lee S., Cheong C., Kang W. and Kim K, Development of high-fidelity numerical methodology
based on wavenumber-frequency transform for quantifying internal aerodynamic noise in critical nozzle,
Applied Science, 2019; 9(14):2885-2899.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022, in Gyeongju, Korea
Extended abstractABS-0538

Transmission loss of three-layered cylindrical silencers lined withporoelastic materials and air
Jongmoo LEE1; Haesang YANG2; Woojae SEONG3
1,2,3

Seoul National University, South Korea

ABSTRACTIn this research, sound transmission loss of a three-layered cylindrical silencer is treated. The silencer isarranged with poroelastic materials and air. Biot model and Johnson-Champoux-Allard-Lafarge (JCAL)
models are applied to analyse wave propagation in poroelastic materials. The boundary conditions between
poroelastic materials and air are obtained. The numerical methods to find modes are explained. Using thesemodes, numerical tests are conducted. Transmission loss of three-layered silencer is observed, and comparedwith the results from commercial finite element method (FEM) code COMSOL. Finally, how the air layer
affects the transmission loss is explained.
Keywords: Biot theory, Silencer, Transmission loss

1. INTRODUCTION
Nennig et al. proposed mode matching method about calculating sound transmission loss of onelayered silencer lined with one poroelastic foam.[1] Lee et al. expanded the mode matching method tomulti-layered silencer with N poroelastic materials.[2] In this research, we deal with a silencer
including two poroelastic materials and air between them. Our goal is to figure out how the air affects
sound transmission loss of the silencer.

2. Waves in a medium
2.1

In AirIn the air domain of Fig.1, linearized wave equation and Euler’s equation hold. Since the shapeof the silencer is cylindrical, the pressure of air toward 𝑟 direction is expressed in a form of linear
combination of Bessel functions i.e 𝑝(𝑟) = 𝐴𝐽 (𝑟) + 𝐵𝑌 (𝑟). In the center of the duct 0 ≤ 𝑟 < 𝑟 ,since the pressure can’t be infinite, B must be zero. But in 𝑟 < 𝑟 < 𝑟 region, B doesn’t vanish.
Consequently, we need 3 unknowns for the two air regions.
2.2 In Poroelastic Materials
We used Biot model to analyse poroelastic waves. There are a lot of material properties requiredin Biot model and it is quite complicated to measure those properties. Johnson-Champoux-AllardLafarge (JCAL) model helps to get effective density and bulk modulus of the saturated fluid ofporoelastic material.[3] We used JCAL model in this research.
Poroelastic waves consist of two compressional waves and one rotational wave. [4] Due to thecylindrical shape of the silencer, each wave is expressed in a form of linear combination of Bessel
functions. Since two coefficients are needed to express each wave and there are 3 waves in aporoelastic material, 6 unknowns are required in every poroelastic material. In our case, there are twosound absorbers in region 𝑟 < 𝑟 < 𝑟 and region 𝑟 < 𝑟 < 𝑟 of Fig.1. Thus, we need 12 unknowns
to express the whole poroelastic waves. Since 3 unknowns existed in the air region, we have total 15
1heisenberg1@snu.ac.kr
coupon3@snu.ac.kr
3
Corresponding author, wseong@snu.ac.kr
2

unknowns to analyse the silencer in Fig.1. In section
3, the boundary conditions will be explained to getthese unknowns.

3. Boundary condition
In our case, the only boundary condition we needis the one between air and poroelastic material
except for the wall condition. It includes threedifferent continuities which is stress continuity, porepressure continuity, and mass flux continuity. [5]Since all equations are linear with respect to thecoefficients of the waves, the boundary conditions
can be expressed in a matrix form 𝐶(𝑘 )𝑋 = 0 ,where 𝑘 is 𝑧 direction wave number, 𝐶 is a
(15 × 15) size matrix for 𝑘 , and X is (15 × 1)
Fig. 1. Shape of three-layered silencer
size vector. In order to make the linear system have
non-trivial solutions, the determinant of 𝐶 must be zero. We can get a lot of modes 𝑘 that makesdet(𝐶) = 0 by solving the equation.

4. Root finding
Solving the equation det(𝐶) = 0 should be done numerically using various root finding
techniques such as Newton’s method or Muller’s method. In this research, we used Muller’s method.
It is easy to find just one root but finding all roots without any missing roots is quite difficult because
we don’t know which initial point will give us which root. However, with adjusting distanceadequately in Muller’s method, it is possible to get a root close to the initial point even on a complex
plane.
Unfortunately, we failed to find roots for a very large silencer due to the round-off error. In thisresearch, round-off error must be dealt with carefully since the matrix 𝐶 has a large condition number.

5. Results and discussion
We conducted numerical tests with a three-layered silencer. The dimension of the silencer is on Table 1.
First, the results from mode matching method (MMM) presented in this research is compared with the resultsfrom commercial finite element method (FEM) code COMSOL. By doing so, we showed the validity of
MMM. Second, we observed the sound transmission loss while changing the volume of the air region
between two sound absorbing materials. We recorded the transmission loss and how its resonance peaks
move. As a result, we found out that if the volume of the air region is too small, the air region doesn’t affectthe sound transmission loss. Moreover, the resonance peaks of the silencer are closely related to the resonancefrequencies of the original expansion chamber without sound absorbers.
L𝑟𝑟

0.315 [m]0.037 [m]0.0762 [m]Table 1. Dimension of the silencer

REFERENCES
1. Nennig B, Perrey-Debain E, Ben Tahar M. A mode matching method for modeling dissipative silencers

lined with poroelastic materials and containing mean flow. The Journal of the Acoustical Society ofAmerica. 2010; 128(6): 3308-3320.
2. Lee J, Yang H, Seong W. Calculating transmission loss of cylindrical silencers lined with multi-layered
poroelastic sound absorbing materials using mode matching method. The Journal of the AcousticalSociety of Korea. 2022; 41(4): 375–388.
3. Allard J, Atalla N. Propagation of sound in porous media: modelling sound absorbing materials 2e.
Chichester, UK: John Wiley & Sons; 2009. Chap. 6.
4. Biot M. A. Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. I. Low-Frequency
Range. The Journal of the Acoustical Society of America. 1956; 28(2): 168-178.
5. Debergue P, Panneton R, Atalla N. Boundary conditions for the weak formulation of the mixed (u, p)poroelasticity problem. The Journal of the acoustical Society of America. 1999; 106(5): 2383-2390.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022 in Gyeongju, Korea

ABS-0044

A compact tonal noise control solution to an electric ducted fan
Tingsheng ZHONG1; Cheng YANG2; Mats ÅBOM3
1

Institute of Vibration Shock and Noise, School of Mechanical Engineering, Shanghai Jiao Tong University,
China

2

Institute of Vibration Shock and Noise, School of Mechanical Engineering, Shanghai Jiao Tong University,
China

3

The Marcus Wallenberg Laboratory for Sound and Vibration Research, KTH Royal Institute of Technology,
SwedenABSTRACTThis study is concerned with reducing the tonal noise emitted by electric ducted fans which is a popular
choice for air mobility vehicles. Different from existing technologies, which are mainly based on lining soundabsorption materials over the duct interior surface, a side-branch tube placed directly over the rotor isinvestigated. The underlying concept is that the aerodynamic pressure fluctuation induced by the rotating
blades drives the tube through its opening and generates a secondary sound field. By carefully adjusting thedepth, opening size and installation position of the tube, the secondary sound field makes a destructive effecton the primary sound field. Considering the space limit encountered by a small electric ducted fan in practicalapplications, an acoustic metamaterial with the same acoustic radiation characteristics as the side-branch tube
is designed and tested. Experimental studies show that the proposed technology offers a space-saving solution
to ducted fan tonal noise problems.
Keywords: Fan tonal noise, Side-branch tube, Acoustic metamaterial

1. INTRODUCTION
Electric vertical takeoff and landing (eVTOL) vehicles attribute to the family of urban air mobility
which have the potential to alleviate urban traffic congestion. Along with the many anticipatedbenefits, there will be noise issues that need to be addressed. This work is dedicated to reducing the
tonal noise at blade passing frequency (BPF) of electric ducted fans which constitute the propulsion
system of the lift fan concept eVTOL.
The periodic motion of the rotating blades generates a considerable amount of tonal noise. For
ducted fans, this type of noise can be reduced by a quarter wavelength side-branch tube that generates
an anti-phase sound to cancel primary sound(1-4). Koopmann and his colleagues(1, 2) studied thepotential of utilizing this secondary sound field to cancel the primary sound field in a centrifugal fan.
In their work, a side-branch tube was mounted at the volute tongue and was driven by the pressure
fluctuation brought about by the passing blades. A secondary sound field with the amplitude equal toand the phase opposite to the primary sound field was produced by carefully adjusting the tube depth,
leading to an effective reduction of the tonal noise. Then, Gorny et al.(3, 4) extended this techniqueto an axial fan casing treatment in which both the BPF and its harmonics noise were reduced byadjusting the opening impedance through perforated plate, the tube depth and the circumferential andaxial position of the tube mounted on the fan shroud. Despite considerable tonal noise reduction wasachieved by this technique, its effectiveness was only demonstrated on a long duct where the higher
order spinning modes are cut off. As for eVTOL applications, a very short duct has to be used due toweight penalty, which increases the complexity of the problem since the higher order duct mod es
12
3

zhongtingsheng@sjtu.edu.cn
cheng.yang@sjtu.edu.cn
matsabom@kth.secannot be effectively attenuated by the duct effect. Furthermore, the confined space of the duct also
appeals for a compact side-branch tube design that fits practical applications(5).
This work is concerned with reducing the BPF noise of an electric ducted fan. Due to the short
inlet and outlet, the installation area for conventional acoustic liner is insufficient so that the side branch tube technique is used as an alternative. The paper is organized as follows. In Section 2,
numerical simulation is performed to examine the shroud pressure fluctuation around the rotor tip
region. In Section 3, a comprehensive experiment is conducted to study influences of the depth,
opening size, circumferential and axial installation position of the side-branch tube on the BPF noise.
Then, the effectiveness of the acoustic metamaterial is designed and tested. Finally, conclusions are
drawn in Section 4.

2. Numerical investigation of the pressure fluctuation on the fan shroud
Computational fluid dynamics simulation was conducted of an electric ducted fan which consistingof 12 rotor blades and 7 stator vanes. The diameter of the rotor is 119.9 mm with a tip clearance of
0.3 mm. Of interest are the amplitude and phase of the pressure fluctuation on the fan shroud that isessential in determining cancellation effect.
The amplitude and phase of the fan shroud pressure fluctuation (at BPF) on a cross-section locatingat half chord length of the rotor blade are shown in Figure 1. The amplitude changes along thecircumferential angle and fluctuates within a range of 5 dB. This is due to the reaction effect on theflow near the rotor tip region when the rotor wakes impinge the stator vanes. It is noted that this effectis not axisymmetric with the largest pressure amplitude occurring near α=0°. This may be explainedby the fact that the stator vane at α=0° used for running motor cables through the duct is thicker thanothers(6). However, the phase (relative to the phase at α=0°) exhibits a periodic pattern with the lobe
number equal to the integer multiple of blade number.
90°

90°

120°

60°

150°

150°

240°

210°

300°

180°

330°

180°

0°

0°

30°

-180°

132

128

124

210°

Pressure Level / dB

30°

180°

60°

Phase of pressure

120°

0°

330°

240°

300°

270°

270°

(a)

(b)

Figure 1 – Variation of the fan shroud pressure fluctuations in the circumferential direction. (a)Amplitude, (b) Phase.
The amplitudes and phases of the fan shroud pressure fluctuation along the axial position at α=180°
are shown in Figure 2. Lower amplitude is found far upstream of the rotor and it gradually increases
when approaching the blade passing region (bounded by dashed lines in the figures) in which the
maximum amplitude occurs near the leading edge of the rotor blade. After that, the amplitudes drop
to the minimum at the position close to the trailing edge. Within the blade passing region, thedifference in amplitude between the maximum and minimum pressures is 28 dB, the phase also
experiences an obvious change with 120°.

80°

130

60°

Blade
Passing
Region40°

Phase of pressure

110
100
90

70
-40

-30

-20

0°
-20°
-40°
-60°

Blade
Passing
Region

80

20°
120°

120

28 dB

Pressure Level / dB

140

-80°

-10
0
10
20
Axial position / mm

30

40

-100°
-40

-30

(a)

-20

-10
0
10
20
Axial position / mm

30

40

(b)

Figure 2 – Variation of the fan shroud pressure fluctuations in axial position (along the magenta line in
the inset). (a) Amplitude, (b) Phase.

3. Reduction of tonal noise in an electric ducted fan using a side-branch tube
The extent to which the cancellation effect is achieved is greatly dependent on the generation of
the secondary sound field. It is well-known that noise is radiated when a flow passes a cavity(7).
When phases of the shed vortices and acoustic perturbations satisfy a particular phase relationship,discrete tones are generated and they are further amplified if the aerodynamic mode of the shear layer
is coupled to the cavity mode(8, 9). For a deep cavity (ratio of opening size to depth much less than1), the resultant sound field is often monopole type near the deep-mode resonance(10). For deploying
noise control treatment near the rotor, it is essential that the technique makes the le ast impact on the
fan aerodynamic performance. Therefore, a side-branch tube with a small opening area is chosen for
the experiment. This geometrically resembles a deep cavity so that a monopole sound field is expected
to be generated.
By using the vortex sound theory, Kook et al.(11) and Zhong et al.(9) have shown that theoscillating flow at the cavity opening is equivalent to a transverse fluctuating force through the
Magnus effect(12). Therefore, the acoustic response of the tube is greatly dependent on the equivalent
aerodynamic loading exerted at the opening. If the resonance frequency (RF) of the side-branch tube
over the rotor is tuned to the BPF, it is possible to generate a secondary monopole sound field andmake a destructive effect on the primary sound field. Since the shroud fluctuation pressure varies
significantly within the blade passing region, the noise cancellation effect of the tube will be sensitive
to its installation position. Furthermore, the tube depth as well as its opening size are also importantin determining the acoustic radiation and thereby the cancellation effect. These parameters will be
investigated in what follows.
3.1 The test rig
Experiment was performed on an electric ducted fan placed in an anechoic chamber. T he rotation
speed of the fan can be adjusted by a speed controller but was fixed at 5520 r/min during theexperiment. The fan radiated noise was measured by 24 microphones (BSWA Type MPA201 freefield) evenly distributed over a circle centred at the geometry centre of the fan, as shown in Figure3(a). The Müller-BBM MKII noise and vibration test system is used for data acquisition. Six
rectangular openings, each having a cross-section of 14 mm×6 mm, are drilled through the shroud
right above the rotor for side-branch tube installation, as shown in Figure 3(b). The six openings allow
an investigation of the circumferential and axial installation position effects on the noise reduction
performance. A 3D printed side-branch tube with a square opening can be mounted on each rectangularopening for fan noise control and an end plug is used to adjust the depth from 0 mm to 139 mm.

Mic-18 Mic-19 Mic-20
Mic-17Mic-21
Mic-16Mic-22Mic-15Mic-24Mic-13

Mic-1

Inlet

Mic-14Mic-12A side-branch tube withadjustable depth

α=180°

Mic-23

R=0.9 m

α=16°
α=8°
α=0°

Mic-2

Mic-11α=-8°
α=-16°

Mic-3

Mic-10End plug

Mic-4

Mic-9

Mic-5
Mic-8

Mic-7 Mic-6

(a)

(b)

Figure 3 – Experimental setup. (a) Measurement points, (b) Tube installation.
3.2 Influence of the tube depth
A side-branch tube with an opening side length of a = 4 mm is fixed at α=−8°, z=0 mm forinvestigating the effect of the tube depth on the BPF noise reduction. As shown in Figure 4(a), theaveraged SPL on the inlet side (Mic-2 to Mic-12) grows with the increase of depth until reaching amaximum. After that, the SPL drops and approaches asymptotically to the baseline case (without theside-branch tube). The variation of the averaged SPL on the outlet side (Mic-14 to Mic-24) follows
the same trend as on the inlet side.
For both sides, the SPL peaks occur when the RF of the tube is tuned approximately to the BPF
where the side-branch tube is expected to have maximum acoustic radiation. In this case, thesecondary sound field makes a constructive effect on the primary sound field on both sides. The SPL
increase on the inlet side is 19.4 dBA which is 8.8 dBA greater than the outlet case, implying that thephase of the secondary sound field is more matching with the primary sound field on the inlet side. If
the RF is further decreased by increasing the tube depth, the SPL drops as a result of two mechanisms:
first, the acoustic radiation of the side-branch tube is reduced due to the frequency mismatch between
the excitation and the tube resonance; second, the phase shift of the secondary sound field. The latter
results in a noise reduction on the outlet side for tube depth greater than 80 mm, implying a destructive
effect from the secondary sound field. Within the range of tube depth under investigation, themaximum reduction of the averaged SPL is 5.6 dBA when the tube depth is set to 104 mm. Since thesound source of a low-speed axial fan can be modelled as distributed dipole sources oriented in thestreamwise direction along its radial span(4, 13), a secondary sound field that is destructive to theprimary sound field on one side of the fan makes a constructive effect on the other side, thereby theincreased SPL.

SPL at BPF / dBA

75
22.5 dBA↑
19.4 dBA↑

70

BPF=RF

a=3 mma=4 mma=5 mm65
a12.0 dBA↑

60
55 Baseline (48.1 dBA)
50
45

0

10

20

30

40

50

60
70
80
Cavity depth / mm

(a)

90

100

110

120

130

140

75

SPL at BPF / dBA

BPF=RF70
65
a60

a=3 mma=4 mma=5 mm

14.0 dBA↑
10.6 dBA↑

Baseline (53.6 dBA)

3.6 dBA↑

55
50
45

0

10

20

30

40

50

60
70
80
90
100
110
120
Cavity depth / mm 4.9 dBA↓ 5.6 dBA↓ 4.8 dBA↓

130

140

(b)
Figure 4 – Influence of side-branch tube depth and opening size on averaged SPL. (a) Inlet, (b) Outlet.
3.3 Influence of the opening size
Also shown in Figure 4 is the effect of the opening size which shows less influence on the
maximum noise reduction. The averaged SPL reductions are 4.9 dBA, 5.6 dBA and 4.8 dBA. In general,
the smaller the opening size, the closer the optimal tube RF to the discrete component of the excitation.
Besides, decreasing the opening size leads to a smaller SPL peak on both sides. Since the SPL peak
results from the constructed effect of the secondary sound field, a decreased SPL peak implies thatthe strength of the secondary sound field decreases with the decrease of the opening size.
3.4 Influence of circumferential installation position
The influence of a side-branch tube (z=0 mm, a=4 mm) installed at different circumferential
positions is shown in Figure 5. Again, the maximum increase of the SPL where the secondary soundfield makes the greatest constructive effect on the primary sound field occurs when the tube RF is
tuned approximately to the BPF, regardless of the circumferential installation position. Th e noise
reduction is observed mainly on the outlet side when the tube RF is shifted away from the BPF. Within
the investigated circumferential positions, the maximum reduction of the averaged SPL is 5.6 dBA
when the tube is installed at α=−8°.

SPL at BPF / dBA

75

α=16°
α=8°
α=0°
α=-8°
α=-16°

α=180°

70
65

α=-16°
α=-8°
α=0°
α=8°
α=16°
α=180°

BPF=RF

60
55 Baseline (48.1 dBA)
50
45

0

10

20

30

40

50

60
70
80
Cavity depth / mm

90

100

110

120

130

140

(a)

SPL at BPF / dBA

75

α=16°
α=8°
α=0°
α=-8°
α=-16°

α=180°

70
65
60

Baseline (53.6 dBA)

α=-16°
α=-8°
α=0°
α=8°
α=16°
α=180°

BPF=RF

1.8 dBA↓

55
50
45

0

10

20

30
40
50
3.4 dBA↓ 2.9 dBA↓

60
70
80
Cavity depth / mm

90

100
110
120
130
140
5.6 dBA↓ 3.1 dBA↓ 3.8 dBA↓(b)
Figure 5 – Influence of side-branch tube circumferential position on averaged SPL. (a) Inlet, (b) Outlet.

3.5 Influence of axial installation position
The influence of the axial installation position for the side -branch tube with α=180° and a=4 mm
is shown in Figure 6. Again, the averaged SPL peak occurs when the tube RF is tuned close to thediscrete component of the excitation. Noise reduction is only observed on the outlet side. For mostaxial positions, the maximum noise reduction occurs when the tube RF is tuned lower than the BPF.
The exception is the z =-4 mm case, where the maximum noise reduction occurs when the RF (tubelength equal to 42 mm) is higher than the BPF. Recall the numerical simulation in Figure 2, thepressure fluctuation experiences a dramatic variation in terms of the amplitude and phase within theblade passing region. Therefore, the phase matching between the primary and secondary sound fields
will be axial position dependent. Within the investigated axial positions, the maximum reduction of
the averaged SPL is 4.3 dBA when the tube is installed at z = 2 mm.
75

SPL at BPF / dBA

z=-2

z=0

19.8 dBA↑ BPF=RF

z=2
z=4

70 z=-4

19.4 dBA↑

z=-4 mmz=-2 mmz=0 mmz=2 mmz=4 mm17.1 dBA↑
13.5 dBA↑

6560

7.6 dBA↑

55 Baseline (48.1 dBA)
50
45

0

10

20

30

40

50

60
70
80
Cavity depth / mm

90

100

110

120

130

140

(a)
75

SPL at BPF / dBA

z=-2

z=0

65

11.7 dBA↑

60

6.9 dBA↑
3.0 dBA↑

Baseline (53.6 dBA)

55
50
45

z=-4 mmz=-2 mmz=0 mmz=2 mmz=4 mm12.2 dBA↑ BPF=RF

z=2
z=4

70 z=-4

9.9 dBA↑

3.8 dBA↓
0

10

20

30

40
50
3.0 dBA↓

60
70
80
Cavity depth / mm

90100
4.3 dBA↓

110

120
130
140
3.8 dBA↓ 2.3 dBA↓(b)
Figure 6 – Influence of side-branch tube axial position on averaged SPL. (a) Inlet, (b) Outlet.
3.6 Reduction of fan tonal noise using an equivalent acoustic metamaterial
To make the proposed technique more applicable for practical use, the side -branch tube is
minimized using the acoustic metamaterial technique. Figure 7 shows an equivalent labyrinth type
acoustic metamaterial for the side-branch tube with a depth of 92 mm. The design criterion is that its
RF is identical to that of the corresponding side-branch tube. In doing so, the thickness of equivalent
acoustic metamaterial is reduced to only 17 mm.

Figure 7 – Schematic of the labyrinth type acoustic metamaterial for controlling.

The noise reduction performance of the designed equivalent acoustic metamaterial is examined on
the electric ducted fan. The SPL directivities of the fan without and with a side-branch tube or its
equivalent acoustic metamaterial are shown in Figure 8. A nearly the same directivity pattern between
the side-branch tube and its equivalent acoustic metamaterial is observed. What’s more, the averaged
insertion loss (IL, defined as the difference in averaged SPL without and with noise reduction
structure) achieved by the equivalent acoustic metamaterial on the outlet side is 4.0 dBA which is 0.3
dBA lower than the side-branch tube case.
90°
120°

60°

150°

60

50

40

30

180°

0°

210°

SPL at BPF / dBA

30°

330°

240°

300°

Baseline
270°
Side-branch tube：Depth=92 mm，IL=4.3 dBA
Metamaterial：Depth=101.2 mm，IL=4.0 dBA

Figure 8 – SPL directivities of the fan without and with a side-branch tube or its equivalent acoustic
metamaterial.

4. CONCLUSIONSThis work studies the tonal noise reduction of an electric ducted fan which has potential use for
eVTOLs. The underlying mechanism is that the primary sound field of the fan is cancelled by thesecondary sound field generated by the side-branch tube over the rotor driven by the aerodynamic
force due to the rotating blades. The effectiveness of the method is examined experimentally on anelectric ducted fan where a significant reduction of the BPF noise can be achieved by carefully
choosing the geometric parameters and installation positions of the side-branch tube. Considering thelimited space allowed for installing noise control treatment on an electric ducted fan in practice, an
acoustic metamaterial with the same acoustic radiation characteristics as the side-branch tube but lessthickness is designed and tested. Experimental results show a good agreement of the SPL
directionalities at the BPF between the two treatments. This implies that an acoustic metamaterial iscapable of achieving the same tonal noise reduction effect as a side-branch tube of the same acoustic
properties.

ACKNOWLEDGEMENTS
This work was supported by National Key Laboratory of Rotorcraft Aeromechanics (No.
61422200201202009), National Natural Science Foundation of China (No. 12004247), a Shanghai
Jiao Tong University - KTH Royal Institute of Technology Collaborative Research and Development
Seed Grant.

REFERENCES
1. Neise W, Koopmann G. Reduction of centrifugal fan noise by use of resonators. J Sound Vib.
1980;73(2):297-308.
2. Koopmann G, Neise W. The use of resonators to silence centrifugal blowers. J Sound Vib. 1982;82(1):1727.
3. Gorny L, Kooopmann G, Neise W, Lemke O. Attenuation of ducted axial propulsors' blade tone noiseusing adaptively tunable resonators. 13th AIAA/CEAS Aeroacoustics Conference (28th AIAA
Aeroacoustics Conference)2007.
4. Gorny L, Koopmann GH. Axial fan blade tone cancellation using optimally tuned quarter wavelength
resonators. J Vib Acoust. 2009;131(2):021002.
5. Cambonie T, Mbailassem F, Gourdon E. Bending a quarter wavelength resonator: Curvature effects onsound absorption properties. Appl Acoust. 2018;131:87-102.
6. Wang J, Huang L. Quantification and control of noise sources in a small axial-flow fan. Noise Control
Eng J. 2006;54(1):27-32.
7. Howe M. Acoustics and aerodynamic sound. Cambridge: Cambridge University Press; 2014.
8. Yang Y, Rockwell D, Lai-Fook Cody K, Pollack M. Generation of tones due to flow past a deep cavity:
Effect of streamwise length. J Fluids Struct. 2009;25(2):364-88.
9. Zhong T, Yang C. Application of the patch transfer function method for predicting flow-induced cavity
oscillations. J Sound Vib. 2022;521:116678.
10. Elder SA. Self-excited depth-mode resonance for a wall-mounted cavity in turbulent flow. J Acoust Soc
Am. 1978;64(3):877-90.
11. Kook H, Mongeau L. Analysis of the periodic pressure fluctuations induced by flow over a cavity. J Sound
Vib. 2002;251(5):823-46.
12. Peters M, Hirschberg A. Acoustically induced periodic vortex shedding at sharp edged open channel ends:
simple vortex models. J Sound Vib. 1993;161(2):281-99.
13. Åbom M, Boden H. A note on the aeroacoustic source character of in-duct axial fans. J Sound Vib.
1995;186(4):589-98.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022 in Gyeongju, Korea

ABS-0107

Validation of hybrid method for fan tonal noise radiation
Wangjian Shu1; Lin Du2; Xiaoyu Wang2; Xiaofeng Sun1
1

School of Energy and Power Engineering, Beihang University, China
2

Research Institute of Aero-Engine, Beihang University, China

ABSTRACTAn integrated computational approach, containing nonlinear harmonic (NLH) method and boundary integral
equation method (BIEM), is developed for the prediction of fan tonal noise. The NLH method is used for thecomputation of acoustic sources, and the BIEM is for acoustic prediction module. The sound propagation in
the cylindrical duct and sound radiation outside the duct can be predicted simultaneously. Then, the approach
is applied to tonal noise prediction of the Advanced Noise Control Fan (ANCF) developed by NASA Glenn
Research Center. The far field acoustic results of the present method are compared with the experimental
measurements and numerical simulations. The accuracy of comparison emphasizes that the present method
is general and efficient for the prediction of fan tonal noise. Three mesh solutions and 2 different turbulencemodels are compared. Then, discussions of aerodynamic and aeroacoustic results in 3 different operating
conditions are demonstrated.
Keywords: BIEM, ANCF, NLH, Tonal noise

1. INTRODUCTION
The emission of noise from aircraft engines is an important issue for increasing environmental
regulations (1). The Ultra-High Bypass Ratio (UHBR) turbofan architecture is promising to be a good
choice for the current generation of aeroengines, and the sound radiation of UHBR has been a research
focus in recent years (2). The tonal noise sources are major components of fan noise, and of whichrotor-stator interaction noise is the main source of tonal noise (3). It is important to predict the rotorstator interaction noise for acoustic evaluation.
The Advanced Noise Control Fan (ANCF) was established for the innovative noise reduction
technologies by NASA over the past 20 years. The ANCF is a low-speed ducted-fan testbed formeasuring and understanding fan-generated aeroacoustic, duct propagation, and radiation to the far
field (4).
Based on the ANCF experimental measurements, many acoustical numerical methods aredeveloped for the validations and verifications. Moreau et al. (2) developed an analytical model forthe prediction of the tonal acoustic source. It is based on rotor wake, which was extracted frommeasurements or flow simulations, and coupled with an analytical cascade response function. The
parameter study, containing the vane sweep and lean angles has been performed, and the optimal
acoustic design is performed.
Daroukh et al. applied the Lattice Boltzmann Method (LBM) to capture aerodynamic and acoustic
features on ANCF (5). Three mesh resolutions have been performed. The LBM simulation wascompared well with the database RANS solution in terms of fan performance, inlet radial flow profile,and outlet radial flow profile, which means that LBM simulations is suitable for mean flow prediction.
The noise prediction is based on acoustic analogy, where the acoustic sources computed by LBM.
However, the tonal noise predicted by the simulation were overestimated by 5 -10dB in average evenwith the fine mesh. This indicated that the LBM is probably difficult to get a reliable tonal signature.
Ferrante et al. developed an innovative computational approach, which integrated CFD andacoustic prediction (6). This approach is integrated in the NUMECA software. The CFD module isbased on an efficient nonlinear harmonic (NLH) method. The sound radiation to the far field iscomputed with the Green’s function approach implemented in a Boundary Element Method (BEM)
12

shuwj@buaa.edu.cn
lindu@buaa.edu.cn

frequency domain solver of the convective Helmholtz equation. For modelling the relevant non uniform background mean-flow, the computational domain was extended, which included the w hole
nacelle duct, the lip and the near field. For acoustic requirements, the element of CFD -acoustic meshdriven by the maximum frequency at least contains 6 points per wavelength. The external boundary
surface of the NLH domain is treated as acoustic source for radiation to far field. The integrated
approach was also applied on ANCF for validations. The far field noise directivities predicted by BEM
are compared with the experimental data, and good agreements are obtained for the tonal noise at first
three harmonics of blade passage frequencies (BPFs).
In this paper, the NLH method is used for the computation of acoustic source of tonal noise, andboundary element integral method (BIEM) with impermeable boundaries are applied for the acoustic
prediction inside and outside the duct. Different from Ferrante’s approach, the harmonic loadings overthe blade surface are treated as acoustic source. The computational source and time are saved. The
accuracy of far field directivities of tonal noise is assessed. The comparison results indicate that thepresent method has the capability to predict the radiation noise at tonal frequencies efficiently.
Furthermore, this method provides a useful way to understand the mechanism of noise generation.
The layout of this paper is as follows. In section 2, the NLH method and BIEM are introduced. To
examine the accuracy of the present model, the ANCF is introduced as an example in section 3. The
verifications and validations of this method are demonstrated in detail. The effect of turbulence modeland mesh resolutions are compared in section 4. Besides, the SPL and directivity pattern of threeoperation conditions are analyzed and discussed. The primary conclusions from this investigation are
given in the last section.

2. NUMERICAL Method
2.1 Nonlinear Harmonic (NLH) method
NLH method, introduced by He and Ning (7), can provide an approximate unsteady solution ataffordable calculation costs. The main idea is that the flow perturbations that make the flow unsteadyare decomposed into a time-average value and harmonics in Fourier series. In this paper, the NLH
method is implemented by NUMECA FINE/Turbo. This approach (8) was shown to be a very efficientsolution method for time periodic flow simulations. In a single stage axial compressor configuration,
the BPFs of the blade rows are the fundamental frequencies of the time periodic disturbances entering
the adjacent blade rows. With the NLH method, the harmonic pressure over blade surface can be castas the acoustic sources. This approach is also used for the computation of acoustic sources generated
by Contra-Rotating Open Rotors (CROR) by Envia (9).
2.2 Boundary Integral Equation Method (BIEM)
The BIEM in this paper is based on Yang and Wang’s derivation (10). The ANCF configuration is
simplified as a finite cylindrical duct with no thickness as shown in Figure 1. The boundary isdispersed into points based on different wavelengths. The BIEM separates the total sound pressure
into the incidence and scattering sound pressure. The sound pressure inside the duct consists ofincidence wave in free field and scattering wave by the boundaries. The boundary is excited by theincidence wave so that the scattering wave is generated. The continuous conditions of sound pressure
and sound particle velocity are applied at the inlet and outlet boundaries. The sound pressure outside
the duct is only the scattering source by the outer boundaries. The incidence wave in free field andscattering wave of BIEM are both implemented by in-house code.

Figure 1 - Sketch of BIEM configuration3. Validations
3.1 Advanced Noise Control Fan (ANCF)
The ANCF is a highly configurable 4-foot diameter ducted fan located in the Aero-Acoustic
Propulsion Laboratory (AAPL) at the NASA Glenn Research Center, as shown in Figure 2 (11).

Figure 2 - Aero-Acoustic Propulsion Laboratory (AAPL) and Advanced Noise Control Fan (ANCF)
The ANCF configuration used in this paper contains 16 rotor blades and 14 stator blades locatedat 1-chord spacing downstream of the rotor (the distance is measured between the rotor blade trailingedge and the stator blade leading edge, at the hub, with chord length of 5.25 inches). The rotational
speed of rotors is 1800 revolutions-per-minute (RPM). Table 1 shows the main characteristics of the
ANCF.
Table 1 – ANCF blade row characteristics
Rotor

StatorNumber of blade

16

14

Radius

0.609m0.610mChord

0.133m

0.114mRotational speed

1800RPM

3.2 CFD Settings
The computational domain of ANCF used in this paper is shown in Figure 3, and it contains thenacelle duct and inlet lip. The CFD mesh generation and calculation used in this paper is the software
NUMECA. The mesh generation refers to Ferrante et al.’s settings (6), and there are 97 flow paths
used in the main channel for rotor blade and 81 flow paths are used in the main channel for the stator
vane. There is no external surface in the near field and the CFD mesh is not to be satisfied for acoustic
requirements. So that the mesh is composed of 3 million nodes, while the mesh in Ferrante et al.’ssimulation is composed of 8 million nodes.

Figure 3 - Configuration and Computational domain of ANCF
The flow model is NLH method (7), and the first three harmonics of BPFs of NLH method are
selected in this paper. The turbulence is modeled by the eddy-viscosity one-equation Spalart-Allmaras
model. Table 2 shows the boundary conditions for the CFD computation.

Table 2 - Boundary conditions

Inlet

Absolute total pressure101325Pa

Absolute total temperature

288.15K

arctan (Vr/Vz)

0arctan (Vt/Vz)

0OutletStatic pressure
101300Pa
With the NLH method and Fourier reconstruction in time, one can obtain the harmonic amplitude
and the instantaneous values of flow field. Figure 4 - Instantaneous entropy field of blade-blade
section at 50% span (left) and at 90% span (right) shows the instantaneous solutions of entropy field
at 50% span and 90% span, respectively. The rotor-stator interaction can be clearly observed at bothradial locations. The harmonic loadings (including real part and imaginary part) over the stator bladesurface are used for the acoustic prediction.

Figure 4 - Instantaneous entropy field of blade-blade section at 50% span (left) and at 90% span (right)
3.3 Comparison of Measurements and Predictions
The far field acoustic directivity of this approach will be compared with the results of experimentmeasurements (13), Daroukh et al.’s simulation (5) and Ferrante et al.’s simulation (6). It should be
noted that there is some difference in the mass flow rate between the operating conditions by different
methods as the Table 3 shows.
Table 3 - Mass Flow of different cases
Case

Present Method

Measurements

Ferrante et al.

Daroukh et al.

Mass Flow (kg/s)
51.44
55.6  1.0
56.3
51.54
The farfield arena designed in an anechoic environment is shown in Figure 5. The simulation
observers are set on an arc ranging from 0 to 90° and located at a distance of 3.66m from the nacelle
inlet.

Figure 5 - The ANCF in the Compact Farfield Arena (left) and Observer locations in far field (right)
The comparison of noise directivity at BPF (480Hz) is shown in Figure 6. The trend of the presentmethod is similar to Ferrante et al.’s results from 0 to 70°. The noise peak of this method is 91dB andat 40° polar angle. The difference between present method and measurements from 10 to 70 ° is within
2dB. The results from 70 to 90° show better agreement with experiment measurements than Ferrante
et al.’s simulation. Even the fine mesh results of LBM show an overestimation about 5 -10dB in
average in whole range.

Figure 6 - Directivity of noise radiation at BPF
The comparisons of noise directivity at 2*BPF (960Hz) are shown in Figure 7. The trend of thepresent method is similar to Ferrante et al.’s results from 0 to 50°. The results of Ferrante et al.’ssimulation seem to be closer to measurements than the present method from 10 to 45°. The fluctuationfrom 50 to 90° by measurements can be predicted by the present method.

Figure 7 - Directivity of noise radiation at 2*BPF
The results from Figure 6 and Figure 7 emphasize that the present method has the capability to
predict the sound radiation of the ducted fan tonal noise. It should be emphasized that the present
method shows high efficiency in time cost compared with the Ferrante et al.’s results (6) and Daroukh
et al.’s simulations (5) as shown in Table 4. The data processing of present method is simplified, andthe required computational time and resource are reduced.
Table 4 - Time cost
MethodPresent

Ferrante et al.

Daroukh et al.

CPU hours

120

480

90,0004. DISCUSSIONS
4.1 Mesh Resolutions
Three mesh resolutions with different flow paths are applied in this paper as shown in Table 5.
Table 5 – Three mesh resolutions
Mesh casemediumfine

finestFlow paths (rotor  stator)
73  57
97  81113  97
The CFD results are dominantly affected by mesh quantity and quality. The comparison of threemesh resolution is shown in Figure 8. The results of three mesh resolutions are the same in trend at
BPF (480Hz), and the difference is within 3dB in amplitude. The results of medium and finest meshresolutions are different from the fine one in directivity trend and amplitude, for example, thedifference can be 3-5dB in average in the range from 20 to 50° at 2*BPF. The fine mesh resolution isaccurate and efficient enough for the ANCF case. The accuracy of acoustic source is as important as
the acoustic propagation model. For further application of the present method in different cases, themesh resolution should be checked.

Figure 8 - Mesh resolutions for noise directivity at BPF (480Hz) and at 2*BPF (960Hz)
4.2 Turbulence Model
Two turbulence model, Spalart-Allmaras (SA) and Shear Stress Transport (SST), are applied on
ANCF. The difference between SA and SST is within 1dB at BPF in whole range, and the differenceat 2*BPF in the range from 55 to 65° is up to 5dB as shown in Figure 9. Considering the noise peakin amplitude, SA model is a better choice for this case.

Figure 9 - Effect of turbulence model for noise directivity at BPF (480Hz) and at 2*BPF (960Hz)
4.3 Operating Conditions
Three operating conditions are discussed in this section. The changes of mass flow led to thevariation of velocity in axial direction. Furthermore, the harmonic loadings on stator, namely the
acoustic source, are altered. For a much more indicative view of acoustic sources, the concentrated
harmonic loading amplitudes by integration over the stator surface are shown in Figure 10. The 1stharmonic loading at BPF decreases as the mass flow increases, while the 2nd harmonic loading shows
the opposite characteristics.

Figure 10 - Concentrated harmonic loading amplitude of stators.
The amplitude of sound radiation shows similar trends according to acoustic sources. As shown in
Figure 11, the directivities of 3 cases show same trend at BPF, however, there is a big difference in therange from 50 to 65° at 2*BPF. It indicates that the distribution of harmonic loading, including amplitude
and phase angle, is altered at 2*BPF more than which at BPF.

Figure 11 - Effect of Mass flow for noise directivity at BPF (480Hz) and at 2*BPF (960Hz)

5. CONCLUSIONSIn this paper, a hybrid CFD-acoustic method is introduced for the prediction of fan tonal noise infrequency domain. The real distributions of harmonic loadings are calculated as acoustic source by
NLH method, and the BIEM is applied for sound propagation and radiation. To validate the accuracyof present method, the ANCF configuration is introduced. The results of sound radiation in far field
are obtained by present method. The comparisons between present method, experiment measurements,
Ferrante et al.’s simulation and LBM simulation show that the present method has the capability to
predict sound radiation generated by fan tonal noise. Then the mesh resolutions, turbulence model andoperating conditions are discussed for their effects to sound radiation. This approach shows the great
efficiency and accuracy, and it can be applied to the prediction of fan tonal noise. For further
investigation, the experiment on a small axial fan will be implemented for further verification of thisapproach.

ACKNOWLEDGEMENTS
This study was supported by the National Natural Science Foundation of China (Nos.52022009
and 51790514).

REFERENCES
1. Hughes C E, Zeug T. NASA / GE Aviation Collaborative Partnership Research in Ultra High Bypass
Cycle Propulsion Concepts[J]. 2008
2. De Laborderie J, Moreau S. Prediction of tonal ducted fan noise[J]. Journal of Sound and Vibration, 2016,
372: 105-132
3. Peake N, Parry A B. Modern challenges facing turbomachinery aeroacoustics[J]. Annual Review of Fluid
Mechanics, 2012, 44: 227-248
4. Sutliff. Advanced Noise Control Fan: A 20-Year Retrospective. 2016.
5. Daroukh M, Le Garrec T, Polacsek C. Low-Speed Turbofan Aerodynamic and Acoustic Prediction withan Isothermal Lattice Boltzmann Method[J]. AIAA Journal, 2021: 1-19.
6. Ferrante P, di Francescantonio P, Hoffer P A, et al. Integrated “CFD-Acoustic” Computational Approachto the Simulation of Aircraft Fan Noise[C]//Turbo Expo: Power for Land, Sea, and Air. American Societyof Mechanical Engineers, 2014, 45608: V02AT41A009.
7. He L, Ning W. Efficient approach for analysis of unsteady viscous flows in turbomachines[J]. AIAA
journal, 1998, 36(11): 2005-2012.
8. Vilmin S, Lorrain E, Hirsch C, et al. Unsteady flow modeling across the rotor/stator interface using thenonlinear harmonic method[C]//Turbo Expo: power for land, sea, and air. 2006, 4241: 1227-1237.
9. Envia E. Aeroacoustic analysis of a high-speed open rotor[J]. International Journal of Aeroacoustics, 2015,14(3-4): 569-606.
10. Yang B, Wang T Q. Investigation of the influence of liner hard-splices on duct radiation/propagation andmode scattering[J]. Journal of sound and vibration, 2008, 315(4-5): 1016-1034.
11. Loew R, Lauer J, McAllister J, et al. The advanced noise control fan[C]//25th AIAA Aerodynamic
Measurement Technology and Ground Testing Conference. 2006: 3150.
12. Sutliff D L. A 20-year retrospective of the advanced noise control fan–contributions to turbofan noise
research[C]//AIAA Propulsion and Energy 2019 Forum. 2019: 3824.
13. McAllister J, Loew R, Lauer J, et al. The advanced noise control fan baseline measurements[C]//47th
AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition. 2009:
624.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022 in Gyeongju, Korea

ABS-0307

A new strategy of designing micro vortex generators to mitigate
tonal noise generation from voluteless centrifugal fan
Martin OTTERSTEN1,2; Hua-Dong YAO2; Lars DAVIDSON2
1

Division of Fluid Dynamics, Department of Mechanics and Maritime, Chalmers University of Technology,
Gothenburg, Sweden
2

Swegon Operations AB, Gothenburg, Sweden

ABSTRACT
Low-speed voluteless centrifugal fans are typically used in ventilation systems. The negative side of the fansis noise, particularly tonal noise of which the dominant tone is at the blade passing frequency (𝐵𝑃𝐹). Oneof the important noise contributors is the gap between the rotating shroud and the stationary inlet duct.
Previous studies have shown that the flow passing through the gap causes turbulence that interacts with theblade leading edge (BLE), rendering surface pressure fluctuations that are the tonal noise sources at 𝐵𝑃𝐹. In
this study, a method of assembling micro vortex generators (MVGs) to control the turbulence for volutelesscentrifugal fans is proposed for the first time. The assembling is made in two different ways: 14 add-ons on
the shroud surface at the gap, and 7 ones on the BLE surface near the shroud. The effects of the MVGs areinvestigated using the hybrid computational aeroacoustics method, which couples the improved delayed
detached eddy simulation method with the Ffowcs Williams and Hawkings acoustic analogy. Our simulations
show that the MVGs are effective to control the turbulence and mitigate the tonal noise. The assembled arrayof 7 MVGs achieves more reduction of the tonal noise than the 14-MVGs array.
Keywords: Tonal noise, Micro vortex generators, Computational aeroacoustics

1. INTRODUCTION
Today most people spend the majority of their time indoors. The indoor environmental quality(IEQ) has become more and more important. When considering IEQ we usually think abouttemperature, CO 2 level, and humidity. However, it has been noticed that sound quality is an importantfactor for good comfort in the indoor environment (1, 2).
Although the internal noise from heating, ventilation, and air conditioning (HVAC) systems isdifficult to isolate, low-speed centrifugal fans installed in the HVAC systems are known as dominantnoise contributors. Nowadays a HVAC system is usually driven by a voluteless centrifugal fan, forwhich a gap (i.e., a clearance) is designed between the rotating fan front shroud and the stationary
inlet duct. The pressure difference between the inner and outer sides of the fan driv es air to passthrough the gap.
There are some previous studies on voluteless centrifugal fans. Both simulations and experiments
were conducted in (3), and it was found that the tonal noise at the blade passing frequency (𝐵𝑃𝐹) is
generated from a helical unsteady inlet vortex that interacts with the rotating blades near the fan
backplate. Another cause is inflow distortion, which leads to flow separation at the blade root near the
backplate (4). In a recent study (5), the present authors found that dominate tones at frequencies
associated with the 𝐵𝑃𝐹 are related to surface pressure fluctuations at the blade leading edge (BLE).
The high surface pressure fluctuations are caused when turbulence stemming from the gap flowinteracts with the BLE close to the shroud.
Micro vortex generators (MVGs) are frequently used to control flow separation (6). They create
vortices that energize the boundary layer and delay separation. As found in a numerical study on windturbines (7), the aerodynamic noise due to trailing edge turbulence is reduced when vortex generators
1

Martin.ottersten@chalmers.seare added. In this paper, it is the first time to propose designing MVGs for centrifugal voluteless fans.
Since the turbulence of this type of fans has different characteristics from wind turbines, it is ofinterest to address whether MVGs are also effective for the fans.
This study aims to investigate how the tonal noise at the 𝐵𝑃𝐹 is affected when MVGs are addedon the centrifugal fan. For the purpose of comparison, the reference fan without MVGs is the same asthat in the previous study (5). Two fans are constructed by adding MVGs at different locations onto
the reference fan. The flows in the current study are simulated using a hybrid method of the improved
delayed detached eddy simulation (IDDES) (8) and the Ffowcs Williams and Hawkings (FW-H)
equation (9). The IDDES is used in the flow simulation, and the FW-H is used for the noise prediction.

2. Configuration
The baseline fan (Case I) and the two modified fans with different MVGs arrangements (Case II
and Case III) are illustrated in Figure 1. Case I is the same fan as the one studied in (5). The fan blades,
shroud, and backplate are the same for all cases. This fan contains 7 blades, and the clearance (i.e.,
the inlet gap) colored in yellow in the figure is located between the stationary inlet duct and therotating shroud. Case II has 14 MVGs placed on the shroud at the gap location, the size and locationof the MVGs are displayed in Figure 1b. Case III has one MVG on each blade, located at the BLE
close to the shroud, the size and location of the MVGs are shown in Figure 1c. As shown in Figure
1a, the fan and inlet duct are positioned within a downstream duct, and the inlet duct is connected to
an upstream duct. This simple geometry layout is designed for the numerical simulations. This
simplification reduces the geometry complexity but retains the principal flow and acoustic
characteristics. The fan parameters are listed in Table 1.

Figure 1. The fan configurations. Gray indicates the rotating fan and brown the stationary inlet duct.
a) The simple geometry layout for the numerical simulations. M1 is the microphone position. The rotation
axis of the fans is the x-axis. The inlet gap is colored in yellow. b) Case II with 14 MVGs along thecircumferential direction on the shroud, and c) Case III with 7 MVGs at the BLEs. The green dash circles
highlight the MVG positions.
Table 1. The fan parameters
d1

d2

d3

d4

b

h1

h2

W

0.165 m0.268 m

0.6 m

1.1 m

0.053 m

4.0 m

2.3 m

1.5 mmThe fan rotation speed is 2800 rpm. Given that the fan has seven blades, the 𝐵𝑃𝐹 is 327 Hz, andthe first harmonics 𝐵𝑃𝐹1 is 653 Hz. The operation point is the same as in (5), where the mass flowrate was set to 0.467 kg/s and that gave a pressure rise of 270 Pa for Case I.

3. Numerical methodology
3.1 CFD method
The air is considered as an ideal gas. The flow is compressible. A finite volume method is utilized
to discretize the continuity, momentum, and energy equations. The method employs a segregated flow
solver accomplished with the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE)
algorithm. All simulations are performed using the commercial software STAR-CCM+ (10). The
turbulence is simulated using the IDDES (11) that is combined with the k-ω SST turbulence model.
This setup has been tested in several studies on rotating machinery (12, 13).
3.2 FW-H equation
A hybrid approach is adopted to predict the noise generated from the flow. In this approach, the
IDDES is coupled with Formulation 1A of Farassat (14). The ambient air density is set to𝜌0 = 1.225 kg/m3, and the speed of sound 𝑐0 = 340 m/s.
According to Neise (15), the fan noise generation at low Mach numbers is dominated by dipole
noise sources that are derived based on the FW-H equation. Hence, the noise prediction in this study
considers only an impermeable integral surface for Formulation 1A. The integral surfa ce consists ofthe fan blades, shroud, and backplate (see Figure 1), while the upstream and downstream ducts, aswell as the fan inlet duct, are neglected. In other words, the acoustic reflection from the duct walls isneglected (16). This treatment is proposed given the fact that the acoustic reflection do not change thetotal power and frequency of the tonal noise, although it influences the sound intensity level becauseof the changed surface area of radiation. Therefore, the general trend of noise level s is still valid when
the reflection is excluded in the analysis.
3.3 Numerical settings
The entire computational domain is divided into stationary and rotating parts. The meshes of thestationary and rotary meshes are not conformable at the interfaces betwee n them. The flux
convergence of the interpolation at the interface between the two meshes has been validated in (16).
The under-relaxation factors for the velocity and pressure in the segregated flow solver are set to
0.7 and 0.4, respectively. The under-relaxation factor for the turbulence equations is 0.7.
The mass-flow boundary condition is set at the inlet with a uniform velocity distribution. The
modeled turbulence intensity is set to 𝐼 = 4% according to 𝐼 = 0.16(𝑅𝑒 )−1⁄8 (10). The modeled
turbulence length scale, ℓ , is set to 0.05 m based on ℓ = 0.7𝑑3 where 𝑑3 is the upstream duct
diameter. The pressure boundary condition is set at the outlet with the static pressure of 0 Pa, and thereference pressure, 𝑝𝑟𝑒𝑓 =101325 Pa, defined in the ambient air. The no-slip boundary condition is
specified on all walls.
The time step is set to ∆𝑡 = 2.0 × 10−5 s, leading to a maximum convective Courant number ofaround 10 in the computational domain. This value fulfills the numerical stability required for the
implicit time-marching method. The maximum number of inner iterations per time step is set to 12.
The sampling period of the noise is 0.3 s for all cases, which includes 14 fan revolutions. This
leads to a frequency resolution of around 3 Hz. The FFT for the spectral calculation of sound pressurelevel (SPL) employs the von Hann window, where 3000 samples are chosen per signal section. The
signal sections do not overlap each other.
Three cut planes (Planes 1-3) across the fan are specified to observe the flow quantities in theanalysis and are shown in Figure 2. The green line is a monitoring line positioned at the BLE.

Figure 2. The cut planes for observing the flow variables. Green line is the monitoring line at the BLE.

4. Mesh
We adopt the same mesh generation strategy that was developed and evaluated in (5), where thefan is the same as Case I. A polyhedral mesh generation method was used to produce prism layers
near the walls and polyhedral cells in the rest of the computation domain. The use of polyhedral cells
for turbomachines has been demonstrated in (16, 17). The mesh parameters are listed in Table 2. The
growth rate is set to 1.05, as suggested in (18). According to the guidelines of the mesh generation
proposed in (5), a local refinement has to be made in the region from the gap to the BLE, and theregion along the joint connection of the blade and the shroud, illustrated in 오류! 참조 원본을찾을 수 없습니다..
Table 2. The mesh parameters
Case I

Case II
6

Case III6

61 × 106

Total number of cells

52 × 10

Number of cells in the rotating zone

41.9 × 106

63.2 × 106

50.9 × 106

Maximum ∆𝑦 + near blade walls

0.73

0.73

0.73

Cell growth ratio

1.05

1.05

1.05

73 × 10Figure 3. Mesh refinement regions (red) at the inlet gap and blades top region.

5. Results and discussion
5.1 Fan performance comparison
The static pressure excluding the reference pressure (𝑝𝑟𝑒𝑓 = 101325 Pa) is displayed along theaxial symmetric line for the three cases in Figure 4. All cases show similar pressure amplitudes in the
upstream duct of the fan, while differences are seen downstream. Case I has the highest pressure andCase III has the lowest. Since the assembled MVGs are the only modifications amongst the fans, these
add-ons are deduced to account for the differences in the pressure rise downstream of the fan.
Important physical quantities describing the fan performance are the time -averaged static pressure̅ . These tworise ∆𝑝̅ , which is between the fan inlet and outlet, and the time-averaged fan torque 𝑀
quantities, as well as the designed mass flow rate 𝑄̅ , are listed for all cases in 오류! 참조 원본을찾을 수 없습니다.. The fan torque increases and the static pressure rise decreases for Cases II and
III compared with Case I.

Figure 4. The pressure along the axial axis of the fan across the computational domain. Here x = −2
corresponds to the location near the outlet and x = 4 near the inlet. The fan location is marked out with thegrey zone.
Table 3. Time-averaged performance parameters of the fan∆𝑝̅ (Pa)̅ (N∙m)𝑀

𝑄̅ (kg/s)

Case I

268

1.13

0.36

Case II

263

1.16

0.36

Case III

257

1.16

0.36

5.2 Comparison of surface pressure fluctuations
The root mean square (RMS) pressures at a monitoring line along the BLE are illustrated for allcases in Figure 5a. Here Plane 3 is in front of the BLE. The detailed information of the plane positions
is referred to (5). The line follows the blade rotation, and the surface pressure is monitored during 12
fan revolutions. The same decaying tendency of the RMS pressures is observed for all three cases. At
the position of the intersection between the shroud and the BLE (Plane 3), all cases present the highest
RMS pressure. When the distance to the shroud increases, the RMS pressure decays to the middle ofthe blade span. Due to the MVGs, local differences exist between these cases. From Plane 3 to Plane
2, Case I is largest, and Case III is lowest. From Plane 1 to the backplate, Cases I and III are nearly
the same. And Case II is smaller than the other cases from the blade middle span to the backplate.
The time-averaged surface pressures at the BLE are shown at different positions for all cases in
Figure 4b. The maximum values in all cases occur at the shroud (Plane 3), whereas at the backplate
the values are negative. The amplitudes of the maximum and minimum pressure, indicated by error
bars in the figure, are largest at Plane 3. They decay when the distance from the inlet gap increases,
which is a general trend for all cases. At Plane 3, Case I has the highest amplitude and Case III thelowest. At Plane 2 the maximum positive fluctuations are larger than the magnitude of the negative
ones, and it is the same for all cases. Case II has the highest amplitude at the backplate. It is clear that
Case III has the smallest pressure fluctuations at the BLE.

Figure 5. a) The RMS of the pressure fluctuations for 12 fan revolutions, on one blade at the monitoring
line; b) the time-average pressure, where the error bars indicate the minimum and maximum pressure.
The contours of vorticity magnitudes ‖𝜔⃗ ‖ in Planes 1, 2, and 3 are shown for all cases in Figure
6. Regions with large vorticity magnitudes are detected at all planes. The area of the large vorticity islargest in Case I, and smallest in Case III. These regions move along the shroud and interact with theBLE. According to (5), surface pressure fluctuations are caused in the physical process that turbulent
vortices stemming from the fan inlet gap interact with the BLE close to the shroud.
Furthermore, it is clear for all cases that the vorticity magnitudes decrease as the distance to theinlet gap increases, namely, from Plane 3 to Plane 1. This phenomenon agrees with the RMS pressure
and time-averaged pressure in Figure 5. The vorticity magnitudes are effectively reduced by Case III.
Correspondingly, the RMS and time-averaged pressure are reduced.

Figure 6. Instantaneous vorticity magnitudes near the shroud are visualized in Planes 1, 2, and 3; a) Case I,b) Case II, and c) Case III.
5.3 Spectral analysis of tonal noise sources
In the previous study of Case I (5), the predicted SPL upstream and downstream of the fan werecompared with experiments. It was shown that the predicted tonal noise at 𝐵𝑃𝐹 and its first harmonicfrequency, 𝐵𝑃𝐹1 had closer agreement upstream (M1) of the fan. Hence, the same microphone
position (M1) is applied to analyze the noise from the fans in this paper. As displayed in Figure 7, thenoise spectra around 𝐵𝑃𝐹 and 𝐵𝑃𝐹1 are compared. At both frequencies, the tonal peaks decrease
with the rank of Case I, Case II, and Case III. This trend agrees with the results in Figures 5 and 6.

Figure 7. The SPL of the sound pressure at the microphone M1 upstream of the fan. The tonal frequency

a) 𝐵𝑃𝐹 = 327 Hz, b) 𝐵𝑃𝐹1 = 653 Hz. The SPL values of the tones are presented.
5.4 Spectral analysis of tonal noise sources
The results of the surface pressure fluctuations at the 𝐵𝑃𝐹 are illustrated for the three cases in
Figure 8. The location of the highest surface pressure fluctuation is at the same position (the BLE
close to the shroud) for all cases. The differences are the magnitude and area with high magnitude s.
In response to the effect that Case I and Case II have the largest sound pressure (see Figure 7), thetwo cases also have the largest area and magnitude for the tonal frequency. The high energy locations
are consistent with the surface pressure fluctuations indicated in Figure 5. As discussed above, thehigh energy is caused by the interaction between the inlet-gap turbulence and the BLE (5).

Figure 8. The SPL of surface pressure fluctuations at 𝐵𝑃𝐹 (327 Hz). From left to right: Case I, Case II,
and Case III.

6. Conclusion
MVGs are designed to control the turbulence from the inlet gap of voluteless centrifugal fans,which are often utilized in HVAC systems. This new design concept is proposed for the purpose of
reducing the tonal noise generation. A standard fan from the previous study (5) is taken as thereference (termed Case I in this paper), which is not installed with MVGs. The designed MVGs areassembled onto the reference fan using two arrangements: 14 MVGs evenly positioned on the shroud
along the circumferential direction and near the inlet clearance (termed Case II), and 7 ones on theblade leading edge near the joint connection of the blade and shroud (termed Case III). These threecases are compared for their aerodynamic and aeroacoustic characteristics. The idea of designing
MVGs is motivated by the findings in a previous study by the present authors, where the gap flow
was addressed as an dominant source of the tonal noise. The flow is simulated using a hybrid method
coupling the IDDES with Formulation 1A of Farassat.
The comparison of the three fans, Cases I–III, shows that adding MVG reduces the pressure risedownstream of the fan but increases the torque. Case II with 14 MVGs near the inlet gap has betterfan performance than Case III with 7 MVGs at the BLE.
The three cases present a similar trend for the RMS pressure, from the inlet to the middle span of
the blade, i.e., the middle of the flow passage. The RMS pressure is largest near the inlet, and decays
as the distance to the inlet gap increases. Case I and III have their lowest values at the backplate. In
contrast, Case II has its smallest value at the middle and as the distance to the gap grows the RMS
pressure increases. Compared to the other cases, Case III overall has lower RMS amplitudes in theflow passage.
High vorticity magnitudes are found near the shroud and BLE surfaces for all three fans. As the
distance to the inlet gap and the shroud increases, the total area of the regions with high vorticity

magnitudes decreases. Moreover, the areas of the three fans decrease in the order of Case I, Case II,
and Case III. It means that the MVGs are effect to reduce the turbulence, especially for the 7 MVG
arrangement near the BLE.
By adding MVG, the aerodynamic and acoustic performances are affected with opposite trends.
The assembling of the MVGs to the BLE (Case III) leads to the higher reduction in generating the tonalnoise at 𝐵𝑃𝐹 and its first harmonic frequency, 𝐵𝑃𝐹1 . However, this worsens the aerodynamic
performance for Case III

ACKNOWLEDGEMENTS
Swegon Operation finances the present work. The simulations were performed on resources
provided by the Swedish National Infrastructure for Computing (SNIC) at C3SE.

REFERENCES
1. Berglund B, Lindvall T, Schwela D. New guidelines for community noise. Noise Vib. Worldwide, 2000;
31:24-29.
2. Azimi M. Noise reduction in building using sound absorbing materials. J. Archit. Eng. Technol. 2017.
3. Wolfram D, Carolus T.H. Experimental and numerical investigation of the unsteady flow field and tone
generation in an isolated centrifugal fan impeller. Journal of Sound and Vibrations, 2010; 329:4380-4397.
4. Sanjose M, Moreau S. Direct noise prediction and control of an installed large low-speed radial fan.
European Journal of Mechanics, 2017; 61:235-243.
5. Ottersten M, Yao H.-D, Davidson L. Tonal noise of voluteless centrifugal fan generated by turbulence
stemming from upstream inlet gap. Phys. Fluids, 2021; 33,. https://doi.org/10.1063/5.0055242
6. Che B, Chu N, Schmidt S.J, Cao L, Likhachev D, Wu D. Control effect of micro vortex generators on
leading edge of attached cavitation. Phys. Fluids, 2019; 31.
7. Gang L, Zhengtao Z, Pingguo Z. Numerical study on noise reduction of wind turbine blade vortex
generators. Conf. Ser.: Earth Environ. Sci 2019; 358.
8. Shur M.L, Spalart P.R, Strelets M.K, Travin A.K. A Hybrid RANS-LES Approach with Delayed-DES and
Wall-Modelled LES Capabilities. International J. Heat and Fluid Flow, 2008; 29:1638-1649.
9. Ffowcs Williams J.E, Hawkings D.L. Theory relating to the noise of rotating machinery. Journal of Soundand Vibration, 1969; 10:10-21.
10. Siemens PLM Software STAR-CCM+ User Guide. Version 12.04, 2017.
11. Salunkhe S, Fajri O.E, Bhushane S, Thompson D, O´Dohety D, O´Dohety T, Mason-Jones A. Validationof tidal stream turbine wake predictions and analysis of wake recovery mechanism. Journal of Marine
Science and Engineering, 2019; 7.
12. Rynell A, Efraimsson G, Chevalier M, Åbom M. Inclusion of upstream turbulent inflow statistics tonumerically acquire proper fan noise characteristics. SAE Technical Paper 2016-01-1811, 2016.
13. Rynell A, Chevalier M, Åbom M, Efraimsson G. A numerical study of noise characteristics originatingfrom a shrouded subsonic automotive fan. Applied Acoustics 2018; 140:110-121.
14. Brentner K.S, Farassat F. Analytical comparison of the acoustic analogy and Kirchhoff formulation formoving surfaces. AIAAA J 1998; 36:1379-86.
15. Neise W. Review of fan noise generation mechanisms and control methods. In: Proceedings of the Fan
Noise 1992 International Symposium, Senlis, France. 1992; 45-56.
16, Ottersten M, Yao H.-D, Davidson L. Unsteady Simulation of tonal noise from isolated centrifugal fan.
Proceedings of Fan Noise 2018 Symposium, Darmstadt 2018.
17. Baris O, Mendonça F. Automotive turbocharger compressor CFD and extension towards incorporating
installation effects. Proceedings of the ASME Turbo Expo 2011: Power for Land, Sea and Air, 2011.
18. Yao H.-D, Davidson L, Eriksson L.E. Surface integral analogy approaches for predicting noise from 3Dhigh-lift low-noise wings. Acta Mech. Sin. 2014; 30:326-338.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022, in Gyeongju, Korea
Extended abstractABS-0736

Performance-based design of low-pressure axial-flow fan using acascade of airfoils
Seo-Yoon Ryu1; Cheolung Cheong1*; Jong Wook Kim2; Byung Il Park2
1

Pusan National University, Republic of South Korea
2

LG electronics, Republic of South Korea

ABSTRACTAn axial-flow fan is frequently used as a cooling fan for an outdoor unit of split-type air conditioners.
Typically, a single airfoil theory is used to design the airfoil sections of fan blades. However, while an axialflow fan rotates, a complex flow field consisting of circumferential and axial flows forms around the fan
blades, making it challenging to apply the single airfoil theory. This study used a cascade of airfoils based on
the blade strip theory to characterize a complex three-dimensional flow field. The computational fluid
dynamic techniques based on finite volume methods were used to predict the flow field, which was
subsequently used as input to the Effowcs Williams-Hawkings integral equation to predict radiated acousticpressure. The validity of the present numerical methods was confirmed by comparing the prediction resultswith the measured ones. Then, two-dimensional flow fields on the cylindrical surface of constant radius fromhub to blade tip were extracted from the three-dimensional flow field. These flow fields around cascades of
airfoils were used to characterize the observed performances of the axial-flow fans. Finally, the pitch anglesof the cascades of airfoils were varied for higher flow rate or efficiency. Then, the selected pitch angles at
each radial section were applied to the existing fan blades. The fan blades redesigned using the current
approach revealed the intended higher flow rate or efficiency. These results confirm that the two-dimensional
approach based on the cascades of airfoils can be used as an effective performance-based design method for
low-pressure axial-flow fans.
Keywords: axial-flow fans, a cascade of airfoils, aeroacoustics, aerodynamics

1. INTRODUCTION
The axial-flow fan generally rotates at a constant rotating speed around the rotation axis,
transporting airflow in a direction parallel to the rotation axis. As the axial-flow fan rotates, airflows
in both the circumferential and axial directions occur around the fan blades. The interaction between
these two flow directions determines the flow rate, efficiency, and aeroacoustic characteristics of anaxial-flow fan, which are the main performances of the axial-flow fan. A lot of studies have been
carried out to improve the performance of the axial flow fan using various design methods. One of
the most common design methods is based on the airfoil theory, which originates from the wing theoryof aircraft. However, the complex flow feature of the axial-flow fan makes it challenging to apply the
airfoil theory as a reliable design tool. An alternative approach is based on the cascade of airfoils (1,2) .
The general design procedure using the cascade of airfoils can be explained as follows. First of all,the basic design parameters, such as the diameters of the fan and hub, the number of blades, andsolidity, are determined. Then, the sectional airfoil shape at each span location is designed using the
airfoil design variables such as camber line, thickness, and pitch angle, which can be classified as
two-dimensional design parameters. Airfoils are stacked along the spanwise baseline, called a stacking
line. In this step, three-dimensional design parameters like sweep and lean angles are also determined.
However, the theory of airfoil cascade is based on the strip theory and thus more appropriate to theconfined configuration. Therefore, it is questionable about the applicability of the airfoil cascade
approach to the axial-flow fans partially covered by the housing structure, where the three* ccheong@pusan.ac.kr

dimensional flow structure affects their performances more significantly. Rye et al. (3) reported that the
winglet shape could significantly affect the performances of axial-flow fans by suppressing the tipvortex flow, a critical three-dimensional flow feature.
This study investigates the applicability of the airfoil cascade approach to improve the performanceof the existing axial-flow fan. The three-dimensional flow of an axial-flow fan used to cool themachinery room in an outdoor unit of the split-type air-conditioner is first simulated using thecomputational fluid dynamic technique. Then, the flow noise is predicted using Effowcs WilliamsHawking integral formula. The validity of the current numerical methods is confirmed through thecomparison of the prediction results with the measured data. Then, the two-dimensional flow on thecylindrical surface of constant radius is extracted and analyzed along with the spanwise direction tocharacterize the observed performances of the fan. These flow fields were reproduced using the twodimensional flow simulation using the cascades of airfoils. Finally, the pitch angles of the cascadesof airfoils are varied for higher flow rate or efficiency. Then, the selected pitch angles at each spanwise
section are applied to the existing fan blades. The fan blades redesigned using the current approachrevealed the intended higher flow rate or efficiency.

2. PERFORMANCE IMPROVEMENT OF FAN USING CASCADE METHOD
Figure 1 shows the axial-flow fan blades with red lines denoting the locations of the airfoil sections
used for the two-dimensional flow simulation using the cascade of airfoils. The axial-flow fan ispartially covered by a fan shroud which is not shown here. The fan blade includes a winglet shape atthe tip, similar to the wingtip fence of the airplane wing, to reduce the tip vortex. The diameter of the
fan is 380 mm. Note that the hub size of the fan is small compared to those of typical axial-flow fans.
Based on this feature, the current fan is named hubless fans. Based on this geometrical feature, thetarget fan can be divided into three sections: hub, mid-span, and tip parts.
The unsteady Reynolds-Averaged Navier-Stokes equations were numerically solved using thefinite volume method based on the unstructured meshes to predict the flow field driven by the fan.
Then, the Effowcs Williams-Hawkings integral equations are solved in combination with the predictedflow field information to predict the radiated acoustic pressure. The validity of the numerical methods
was verified by comparing the predicted results with the experimental results. The distributions of
aerodynamic loadings and efficiency of airfoil sections were calculated and analyzed along the
spanwise direction from hub to tip. It was found that the blade sections belonging to the mid-span
region play dominant roles in exerting flow loadings of thrust and torque. From the result, the sectional
airfoil shapes in the mid-span part are selected for further analysis using the airfoil cascade.
Figure 2 illustrates the geometrical procedure of extracting a cascade of airfoils from the blade ata constant radius. To reproduce the axial and circumferential flows that occurs as the fan rotates, theextracted cylindrical area at the constant radius was used as the computational domain for the twodimensional simulations using the cascade of airfoils. The variations of the thrust and torque of thecascade airfoils were examined by changing design parameters such as camber inlet and outlet angles
of sectional airfoils. Figure 3 compares the flow fields of the original and optimal configurations of
the cascade airfoils in terms of vorticity magnitude. It can be seen that the flow of the optimized airfoil
is more aligned with its chord line so that the vortex shedding at the trailing edge is reduced incomparison with that of the original one. Finally, the three-dimensional fan constructed by employing
the airfoil shapes obtained for the simulations using the cascade of airfoils revealed improved
performances. These results confirm that the two-dimensional approach based on the cascades of
airfoils can be used as an effective performance-based design method for low-pressure axial-flow fans.

Figure 1 – Target axial-flow fan with airfoil sections

Figure 2 – Geometrical process for extracting cascade of airfoils using cylindrical section

Figure 3 – Snapshots of vorticity magnitude between original (left) and optimized airfoil(right)

ACKNOWLEDGEMENTS
This study was carried out through the research projects supported financially by LG Electronics.

REFERENCES
1. Batyaev, E.A., Kurzin, V.B. Method of optimization of blade shapes in aerodynamic design of the fancascade. J Appl Mech Tech Phys. 2002;43:407-705
2. Zhang, S., Yang, B., Xie, H., Song, M. Applications of an improved aerodynamic optimization method
on a low Reynolds number cascade. Processes. 2020;8(9):1150
3. Ryu, S. Y., Cheong, C., Kim, J. U., Park, B. I., Park, S. M. Numerical and experimental investigation on
effects of blade tip-rake on vortex structure and aerodynamic noise of axial-flow fans in an outdoor unitof air-conditioner. Universitätsbibliothek der RWTH Aachen. 2019
4. Chen, K., Liu, Q. P., Sun, W. L. Experiment research on the efficiency of bionic blade of axial fan. IEEE
international conference on mechatronics and automation 2018. p. 94-98.

ABS-0192

Aeroacoustic analysis of port noise by using a three-dimensional numericalmodel of a bass reflex speaker system
Kaisei URYUU(1) , Ryoya TABATA(1) , Taijiro OHNO(1) , Takeshi NANRI(2) , Taizo KOBAYASHI(2) , Kin’ya Takahashi(1)(1) Kyushu Institute of Technology, Japan, takahasi@phys.kyutech.ac.jp(2) Kyushu University, Japan, tkoba@cc.kyushu-u.ac.jp

ABSTRACT
We numerically study port noise observed for a bass reflex speaker system with a compressible fluid solver,
Large-Eddy Simulation(LES), to explore the noise generation mechanism from the viewpoint of aeroacoustics.
The port noise is considered an aerodynamic sound generated by vortices, created by the interaction between
the acoustic field and port opening. However, the detail of the sound generation mechanism is still an open
problem. By using a 3D-model, the port-noise is well reproduced by compressible LES, when the speakersystem is acoustically driven at its resonance frequency, the Helmholtz resonance frequency of the bass reflex
speaker system. Vortices are created near the edges of the port and generate broadband noise. However, noises
are enhanced due to resonance in some bands, which correspond to the acoustic resonance frequencies of the port
and encloser themselves. We are also planning to investigate the noise generation mechanism by using Howe’s
energy corollary, which allows us to estimate the energy transfer between fluid dynamics and acoustics, namely
we consider the problems of where the aeroacoustic noise is generated and how much energy is transferred fromthe vortex motions to the acoustic field.

Keywords: bass-reflex port, Helmholtz resonance frequency, compressible LES, Finite-difference timedomain, Howe’s energy corollary

1

INTRODUCTION

The bass reflex system is now widely used in household and professional loudspeaker systems to increase
low-frequency efficiency. Such a loudspeaker mainly consists of a speaker unit, a port and an enclosure thatsurrounds it. The port connects the air inside the enclosure to the outside, and these two objects construct a
Helmholtz resonator. This system inverts in phase the low-frequency portion of the sound generated from therear of the speaker unit and radiates it from the port exit in the same phase as the sound generated at thefront of the unit, thereby enhancing the sound in the low frequency range. However, the bass-reflex systems
have a drawback: they produce an unpleasant noise called ’port noise’, whose mechanism should be clarified
from the viewpoint of aeroacoustics. Roozen et al. showed that at high sound pressure levels, bass-reflex ports
produce a blowing sound, which is caused by the acoustic flow swirling at the edge of the port where the flow
velocity is high, and acoustic standing waves in the longitudinal direction of the port are pulsatilely excitedby periodically generated vortices [1]. Garcia-Alcaide et al., numerically studied two-dimensional axisymmetricgeometry models to reproduce port noises compared with experimental results[2]. They found that the amplitude
of noise is enhanced in a certain bandwidth when the port is opened and it is driven at frequencies near theHelmholtz frequency, and concluded that the origin of the noise is aeroacoustical [3, 4]. From these previous
results, we can assume the following scenario of ’port noise’ generation process when driven at frequencies near
the Helmholtz frequency: 1) An acoustic flow with a low frequency is locally regarded as an almost uniform
fluid flow in a short time interval, and the interaction of the acoustic flow with the edges of the pipe induces
vortex shedding; 2) Such vortices generate aeroacoustic wideband noise; 3) noise components are enhanced ina particular range which involves the resonance frequencies of the pipe and enclosures. Of course, the details

(a)

(b)

Figure 1. 3D-model of a bass-reflex speaker drawn by a 3D-CAD and a cross-sectional view at z = 0 (a)Three-dimensional model. (b) Cross-sectional view at z = 0: Ol = Od = 600mm, Oh = 300mm, Pl = Pd = 10mm,
Ph = 50mm, Cl = Cd = Ch = 70mm.
of the noise generation mechanism remain unresolved to this day and should be clarified from the viewpoint of
aeroacoustics.
In this study, we numerically studied a 3D-model of a bass-reflex speaker with a compressible fluid solver,
Large-Eddy Simulation (LES), which reproduces acoustic and fluid fields simultaneously. We checked the reliability of our simulations, observing the acoustic and fluid fluctuations inside and outside the model system
when driven by the Helmholtz resonance frequency. Then, we confirmed our scenario of ’port noise’ generation
process. It is known that Howe’s energy corollary (HEC) introduced by Howe is a practically reliable method
to estimate the energy transfer between the acoustic and fluid fields[4, 5, 6, 7, 8, 9, 10]. Then, HEC can beapplicable to the study of bass reflex speaker systems to consider the problems of where the aeroacoustic noiseoccurs and how much energy is transferred from the vortex motion to the acoustic field. For the preparation of
future work by using HEC, we calculated acoustic oscillations at the Helmholtz resonance by using an acoustic
solver, the Finite-difference time-domain (FDTD) method [11], because data of the acoustic field separated fromthose of the fluid field are required to implement HEC [4, 5, 6, 7, 8, 9, 10].

2

MODEL AND NUMERICAL METHOD

2.1 Model and Compressible fluid solver
To focus on the nature of aerodynamic sound induced by the action of bass reflex ports, we ignored a direct
sound driven by the front side of a diaphragm of a speaker unit. Thus, our model is a Helmholtz resonatordriven by a sound source attached to an inside wall. Figure 1 shows a 3D-model of a bass-reflex speaker anda cross-sectional view at z = 0, where the origin of the coordinate is set at the center of the bottom wall of theenclosure, and the x-axis and y-axis are horizontal and vertical lines, respectively, so the z-axis is in the depth
direction. A cube at the bottom is an enclosure and an upper rectangular parallelepiped is an exterior domain.
Then, a narrow channel connecting them is a port. Normally, the port is located inside the enclosure, but inthis model, the port is simply set outside of the enclosure body and connected to it for numerical convenience.
It is known that gradually widening the port toward both ends, namely reducing the cross-sectional area in thecenter of the port can reduce noise [1]. Although a straight port creates more noise, it is rather suitable forinvestigating noise generation mechanisms due to its simple geometry. Thus, we adopt the model shown in
Figure 1.
A driving source is set on a center area of 20mm × 20mm of the bottom wall of the enclosure, and mimics
the motion of a diaphragm such that a time dependent flow is applied from this area with velocity
v = V0 tanh(t/τ) × sin(2π f t),(1)

Figure 2. Cross section of Three-dimensional mesh at z = 0.
where the maximum amplitude V0 is set as V0 = 0.1m/s, and the parameter τ controlling a transient time is set
as τ = 0.005s. Thus, for t  τ, the flow becomes periodic with the amplitude V0 and with a frequency f . The
frequency f is set as Helmholtz resonance frequency f = 119.7929Hz, which was given as
s
S0
c0
,
(2)
f=
2π Le f f V
where the speed of sound c0 is set as c0 = 347.127m/s, V denotes the volume of the enclosure of 70 × 70 ×
70mm3 , and the port has a crosssection of S0 = 10 × 10mm2 and an effective length including
the end corp
rections, which is given as Le f f = 59.591mm. Here, the end correction is given as re f f = S0 /π, where thesquare cross section of the port is replaced by a circle with the same area of a radius r. Since the port has two
open ends, the end correction ∆l is given as ∆l = 2re f f . Thus, the effective length of the port is obtained as
Le f f = ∆l + l.
For numerical calculation, we used compressible Large Eddy Simulation (LES), which reproduces fluid andacoustic fields simultaneously. In LES, eddies larger than the mesh size are calculated directly by the NavierStokes equations, while the effect of eddies smaller than the mesh size is estimated by using a statistical model(SGS model). Practically, we adopted ’rhoPimpleFoam’ with an SGS model ’one-equation eddy’ in OpenFOAM.
Figure 2 shows a cross-sectional view at z = 0 of the numerical mesh with representative observation points.
Table 1 shows the coordinates of the observation points in Figure 2. For the enclosure and port, an isotropic
mesh with the interval of 0.5mm is used, but for the exterior domain, the mesh is expanded like a spider
web shape to reduce the number of cells, which has a central core of the isotropic mesh with a volume of
200mm × 100mm × 200mm. Table 2 shows the mesh parameters and time step, and Table 3 shows the valuesof physical parameters of the compressible fluid. The simulations were performed on 16 nodes each with 36
cores (576 parallel threads) of the high-performance computer cluster ITO (subsystem A) at Kyushu University.
Table 1. Representative observation points
c1

p2

p3

p4

o5

o6

(0, 0.035, 0)(0, 0.07, 0)(0, 0.095, 0)(0, 0.12, 0)(0, 0.155, 0)(0, 0.19, 0)Table 2. Mesh parameters and time step
Number of grids

minimum grid size

Time step ∆t

34, 784, 000

0.5mm

2.5 × 10−9 s

Table 3. Physical parameters of compressible fluid
parameters
valuesDensity at rest ρ03

1.162kg/m

Viscosity µ

Sound speed c0

1.846 × 10−5 Pa · s

347.127m/s

2.2 Acoustic solver
To implement Howe’s energy corollary(HEC), one needs data of the acoustic field separated from those of thefluid field [4, 5, 6, 7, 8, 9, 10]. For the preparation of HEC, we reproduced an acoustic field in the Helmholtz
resonance with an acoustic solver, Finite-Difference-Time-Domain (FDTD) method, for which the partial differential equations are discretized in time and space, and calculations are performed using the difference method[11]. The governing equations are given by∂~v= −∇p,∂t1∂p∇ ·~v = −
,
k ∂t
ρ

(3)
(4)

where ~v and p denote the acoustic particle velocity and acoustic pressure, and ρ and k are the air density at
rest and the volume modulus, respectively. In this paper, we used a solver of second order in time and of fourthorder in space, the FDTD(2,4). The discretized equations are expressed as11n− 1(i + , j, k) = vx 2 (i + , j, k)
2
2
k2
k2
∆t
{k1 pn (i + 1, j, k) − k1 pn (i, j, k) − pn (i + 2, j, k) − pn (i − 1, j, k)},(5)−
ρ(i, j, k)∆x
3
3
1
1
n+ 1
n− 1
vy 2 (i, j + , k) = vy 2 (i, j + , k)
2
2
∆t
k2
k2
(6)
−
{k1 pn (i, j + 1, k) − k1 pn (i, j, k) − pn (i, j + 2, k) − pn (i, j − 1, k)},ρ(i, j, k)∆y
3
3
1
1
n+ 1
n− 1
vz 2 (i, j, k + ) = vz 2 (i, j, k + )
2
2
∆t
k2
k2
−
{k1 pn (i, j, k + 1) − k1 pn (i, j, k) − pn (i, j, k + 2) − pn (i, j, k − 1)},(7)
ρ(i, j, k)∆z3
3k(i, j, k)∆t1
k2 n+ 13
k2 n+ 13
n+ 1
pn+1 (i, j, k) = pn (i, j, k) −{k1 vx 2 (i − , j, k) − vx 2 (i + , j, k) + vx 2 (i − , j, k)}
∆x
2
3
2
3
2
k(i, j, k)∆t1
k2 n+ 123
k2 n+ 123
n+ 21−
{k1 vy (i, j − , k) − vy (i, j + , k) + vy (i, j − , k)}
∆y
2
3
2
3
2
1
1
1
k(i, j, k)∆t
1
k
3
k
3
n+
2 n+
2 n+
−
{k1 vz 2 (i, j, k − ) − vz 2 (i, j, k + ) + vz 2 (i, j, k − )},
(8)
∆z
2
3
2
3
2
n+ 12

vx

where vx , vy , vz denote the acoustic particle velocities in the x, y, z directions, respectively, ∆x,∆y and ∆z are thespatial grid spacings in x,y and z directions, respectively, ∆t is the time increment, and i, j, k are the numbersof grid points in x, y, z directions, respectively.

Figure 3. Cross-sectional view of 3D model at z=0 in FDTD : O0h = 350mm, O0w = 360mm, Al = 4.2mm,
Pl = Pd = 10mm, Ph = 50mm, Cl = Cd = Ch = 70mm.
The computational grid was a staggered grid, in which the grid points of the sound pressure and those of
the acoustic particle velocity are shifted half a grid apart from each other. We set the walls of the model suchthat they contain grid points of the flow velocity. Thus, the nearest gird points of the sound pressure are awayfrom the wall by half a gird interval. On the wall, the normal component of ~v takes a value of zero.
The boundary of the outer region must be transparent except for the bottom plane. In reality, the transparency of the boundary is not perfect and a portion of the outgoing wave is reflected inward. To solve thisproblem, the PML absorbing boundary condition was adopted because this is a reliable method[10].
Figure 3 shows a cross-sectional view of the 3D-model for FDTD at z = 0. Except for the PML absorbing
boundary area of width Al , the dimensions of the model are the same as those in Figure 1. The grid interval
is 0.5mm in the whole region, i.e., enclosure, port and exterior domain. In the case of compressible fluid
simulation, a driving source was set on a center area of 20mm × 20mm of the bottom wall of the enclosure.
However, for the convenience of controlling the amplitude of the sound wave, we put a pressure source insteadof a velocity source, which is given by
p0 = P0 tanh(t/τ) × sin(2π f t),(9)where τ and f take the same values as those for LES, and the pressure amplitude P0 is determined by the
result of the compressible fluid simulation, namely P0 = 420.8925Pa. The other physical parameters are thesame as those for the compressible fluid simulation. Table 4 shows the mesh parameters and time steps. In thissimulation, we took the density of air at rest and the speed of sound as ρ = 1.159kg/m3 and c0 = 347.610m/s.
Table 4. Mesh parameters and time step of FDTD
Number of grids

grid size

Time step ∆t345, 784, 000

0.5mm

1.0 × 10−9 s

(a)

(b)

(c)

(d)

Figure 4. Pressure and velocity distributions (a) Pressure distribution at t = 0.04417s. (b) Pressure distribution
at t = 0.0483s (c) Velocity distribution at t = 0.02924s. (d) Velocity distribution at t = 0.05433s

3

Numerical results

3.1 Compressible fluid simulations with LES
In this subsection, we show the results of compressible fluid simulations with LES. Figure 4 shows the pressure
distributions at t = 0.04417s and t = 0.0483s and the velocity distributions at t = 0.02924s and t = 0.05433s.
In a stationary state, strong pressure oscillations were observed in the enclosure. This indicates that the bassreflex system acts as a Helmholtz resonator. An oscillating high-velocity flow was observed in the port. In time
evolution, vortex rings were emitted from the inlet and outlet of the port, which collapsed into smaller vortices
as they moved away from the port. This vortex shedding from the ends of the port was reported by Roozen et al.
and Garcia-Alcadie et al. [1, 2]. Figure 5 shows the fluctuations of pressure at representative points. As shownin Figure 4, strong pressure fluctuations with the Helmholtz resonance frequency were observed at the points c1
and p2 in the enclosure and the amplitude of the fluctuation decreased toward the exterior domain in the port.
The fluctuations at the points o5 and o6 in the outside were smaller in amplitude than those in the enclosure
and port, and were disturbed due to the vortex rings. The observation of the pressure fluctuations indicates thatthe system was in the Helmholtz resonance. The fluctuations of the flow velocity at the representative points
are shown in Figure 6. The fluctuations with large amplitude were observed at the points p2 . p3 and p4 in
the port because it has a narrow channel. On the other hand, the fluctuations at the point c1 in the enclosureand at the points o5 and o6 in the exterior domain were irregular in greater or less degree probably due to the
disturbances of the vortex rings.
To estimate the ’port noise’, the power spectrum of the pressure fluctuation at the point o5 near the port exit
was calculated. The result is shown in Figure 7. There were remarkable peaks in a range of 2300Hz ∼ 3000Hz.

(a)

(b)
p
100400100200100200p [Pa]

p [Pa]

p
100400100000100000

99800

99800

99600

99600
0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0

0.01

0.02

0.03

Time [sec]

0.04

0.05

0.06

0.07

0.08

Time [sec]

(c)

(d)
p
100400100200100200p [Pa]

p [Pa]

p
100400100000100000

99800

99800

99600

99600
0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0

0.01

0.02

0.03

Time [sec]

0.04

0.05

0.06

0.07

0.08

Time [sec]

(e)

(f)
100010100010p

100005p [Pa]

p [Pa]

100005

100000

99995

99990

p

100000

99995

0

0.01

0.02

0.03

0.04

0.05

Time [sec]

0.06

0.07

0.08

99990

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Time [sec]Figure 5. Pressure oscillations at the observation points . (a) Observation point c1 . (b) Observation point p2 .
(c) Observation point p3 . (d) Observation point p4 . (e) Observation point o5 . (f) Observation point o6 .

(a)

(b)
0

10

U

U

-1
5

U[m/s]

U[m/s]

-2

-3

0

-4
-5
-5

-6

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

-10

0.08

0

0.01

0.02

0.03

time [sec]

0.04

0.05

0.06

0.07

0.08

time [sec]

(c)

(d)
10

10

U

5

U[m/s]

U[m/s]

5

0

-5

-10

U

0

-5

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

-10

0.08

0

0.01

0.02

0.03

time [sec]

0.04

0.05

0.06

0.07

0.08

time [sec]

(e)

(f)
6

5

U

5

U

4

4

U[m/s]

U[m/s]

3
3
2
1

2

1

0
0
0

0.01

0.02

0.03

0.04
time [sec]

0.05

0.06

0.07

0.08

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

time [sec]Figure 6. Velocity oscillations at the observation points . (a) Observation point c1 . (b) Observation point p2 .
(c) Observation point p3 . (d) Observation point p4 . (e) Observation point o5 . (f) Observation point o6 .

Figure 7. Power spectrum of the pressure oscillation at the point o5 .
These frequency components should be enhanced by resonance states of the port and enclosure. The resonant
frequency of the fundamental mode f p for the port and the frequency of the fundamental mode fe for theenclosure were approximately obtained as
fp

=

fe

=

c0
≈ 2913Hz,
2Le f fc0
≈ 2480Hz.
2Ch

(10)

Although the frequencies of the peaks observed numerically did not coincide with f p and fe , it is safe to saythat broadband noises created by the vortex shedding at both ends of the port were enhanced in a range near
the resonance frequencies of the port and enclosure like cavity flow noise. Note that it is not an easy task tocorrectly obtain the resonance frequencies related to the enclosure and port, because they are connected portionsof the Helmholtz resonator and are not isolated from each other.
3.2 Acoustic simulations with FDTD
In this subsection, we discuss the results of acoustic simulations with FDTD. The observation points are thesame as those in Figure 2. Figure 8 shows the fluctuations of acoustic pressure and acoustic particle velocity
at the points c1 and p3 . The oscillations have almost reached stationary states but spent a longer time attaining
stationary oscillations compared with those in the fluid simulation. This is probably because a transient period
becomes longer due to a larger value in the quality factor, namely less dissipation. Actually, the acoustic
simulation does not include drag force caused by fluid viscosity and only suffers from radiation loss.
The amplitude of pressure oscillation took the same value as that in the fluid simulation at each observation
point and the velocity oscillation at the point p3 was the same in amplitude as that in the fluid simulation.
However, at the point c1 , the velocity oscillation in the fluid simulation was very unstable due to a disturbanceof vortices caused by the interaction of the acoustic field with the edge of the pipe, while that in the acoustic
simulation was very stable due to no disturbance of vortices. This means that the Helmholtz resonance state
was successfully reproduced with FDTD in terms of acoustics.

4

CONCLUSIONSIn this paper, to explore the generation mechanism of ’port noise’ observed for bass-reflex speaker systems
from the viewpoint of aeroacoustics, we numerically studied a 3D model with compressible LES. To focus on
the nature of aerodynamic sound induced by the action of bass reflex ports, a direct sound driven by the front

(a)

(b)
P

Uy

400

0.1

Flow Velocity [m/s]

Pressure [Pa]

200

0

-200

0.05

0

-0.05

-0.1

-400
0

0.02

0.04

0.06

0.08

0.1

0.12

0

0.02

0.04

Time [sec]

(c)

0.08

0.1

0.12

(d)
P
200

10

100

5

Flow Velocity [m/s]

Pressure [Pa]0.06
Time [sec]

0

-100

-200

Uy

0

-5

-10
0

0.02

0.04

0.06
Time [sec]

0.08

0.1

0.12

0

0.02

0.04

0.06

0.08

0.1

0.12

Time [sec]Figure 8. Fluctuations of acoustic pressure and acoustic particle velocity at the observation points c1 and p3 .
(a) Pressure at the point c1 . (b) Velocity at the point c1 . (c) Pressure at the point p3 . (d) Velocity at the pointp3 .

side of a diaphragm of a speaker unit was ignored in our model; thus, the model was a Helmholtz resonatordriven by a sound source attached to an inside wall. The acoustic oscillation of Helmholtz resonance as wellas the aeroacoustic noise, ’port noise’, were successfully reproduced. Vortex rings emitted from both edgesof the port, which should generate aeroacoustic noise, were also observed. We also confirmed that the noise
is enhanced in a particular range due to the influence of the acoustic resonances of the port and enclosure.
Even though it is an indirect way, these results give numerical evidence for our assumption that the interactionof an acoustic flow of a low frequency with the edges of the pipe induces vortex shedding, such vortices
generate aeroacoustic wideband noise, and noise components are enhanced in a particular range which involves
the resonance frequencies of the pipe and enclosures.
As preparation for the analysis based on Howe’s Energy Corollary (HEC) [4, 5], we also implemented an
acoustic simulation using the FDTD method and confirmed through the observation of the pressure and velocity
that the Helmholtz resonance state can be reproduced with FDTD. The calculation still continues to obtain dataof enough length. Let us show our future plan. By using HEC, we can estimate the energy transfer betweenhydrodynamic and acoustic fields [4, 5, 6, 7, 8, 9, 10] (see Appendix A). Then, to clarify the noise generation
mechanism, we will consider the problems of where the aero-acoustic noise is generated and how much energy
is transferred from the vortex motion to the acoustic field.

ACKNOWLEDGEMENTS
The present work was supported by Grant-in-Aid for Scientific Research (C) Nos. 19K03655 from the Japan
Society for the Promotion of Science (JSPS) and “Joint Usage/Research Center for Interdisciplinary Large-Scale
Information Infrastructures” and “High Performance Computing Infrastructure” in Japan (Project ID: jh220001).

A

Howe’s Energy Corollary (HEC)

To estimate the energy transfer between hydrodynamic and acoustic fields, Howe introduced the following
formula[4, 5]
ZZZ
ZZZ
1 ∂
~ × v~w ) ·~u dV,
ρ0v~w 2 dV ≈ ρ0
(ω
(11)
Π=
2 ∂t
V
V
~ and ~u are the solenoidal fluid velocity, vorticity and acoustic particle velocity, respectively. Π
where v~w , ω
gives the change in kinetic energy of the fluid field in volume V and is approximated as an integral of the innerproduct of the Coriolis force density and the acoustic particle velocity. When Π is positive, the sound energy
is converted to fluid energy, and when Π is negative, the energy transfer occurs oppositely. To implement
HEC, one should prepare data of the acoustic field isolated from the fluid field [6, 7, 8, 9, 10]. To do thisapproximately, we reproduce the acoustic field with FDTD[9, 10]. Then, we can estimate the energy transfer
between acoustic and fluid fields near the port, to investigate ’port noise’ generation mechanism.

REFERENCES[1] Roozen NB, Bockholts M, van Eck P, Hirschberg A. Vortex sound in bass-reflex ports of loudspeakers. Part
I. Observation of response to harmonic excitation and remedial measures. J Acoust Soc Am. 1998; 104:
1914-1918.
[2] Garcia-Alcaide VM, Palleja-Cabre S, Castilla R, Gamez-Montero PJ, Romeu J, Pamies T, Amate J, Milan
N. Numerical study of the aerodynamics of sound sources in a bass-reflex port. Eng. Appl. Comput. Fluid
Mech. 2017; 11: 210-224.
[3] Lighthill MJ. On sound generated aerodynamically. Part I: General theory. Proc. Roy. Soc. London A. 1952;
211: 564-587.
[4] Howe MS. Acoustics of Fluid-Structure Interactions. Cambridge, UK: Cambridge Univ. Press; 1998.
[5] Howe MS. On the absorption of sound by turbulence and other hydrodynamic flows. IMA J Appl Math.
1984; 32: 187-209.

[6] Bamberger A. Vortex sound in flutes using flow determination with endo-piv. Proc Forum Acusticum Budapest 2005; 29 August- 2 September; Budapest, Hungary 2005 p.665-670.
[7] Finnegan SL, Meskell C, Ziada S. 2010 Experimental investigation of the acoustic power around two tandem
cylinders. J Press Vess Technol. 2010; 132: 041306.
[8] Yoshikawa S, Tashiro H, Sakamoto Y. Experimental examination of vortex-sound generation in an organ
pipe: A proposal of jet vortex-layer formation model. J Sound Vib. 2012; 331: 2558-2577.
[9] Kobayashi T et al. Interaction between compressible fluid and sound in a flue instrument. Fluid Dyn. Res.
2014; 46: 061411[10] Tabata R, et al. Three-dimensional numerical analysis of acoustic energy absorption and generation in an
air-jet instrument based on Howe’s energy corollary. J Acoust Soc Am. 2021; 149: 4000-4012.
[11] Sendo Y, Kudo H, Kashiwa T, Ohtani T. The FDTD(2, 4) method for highly accurate acoustic analysis inthree-dimensional space. Electronics and Communications Jpn Part 3. 2003; 86: 30-37.

ABS-0250

Compressible ﬂuid analysis on basic properties of a thermoacoustic equipment

Yo TASHIMA(1) , Taijiro OHNO(1) , Takeshi NANRI(2) , Taizo KOBAYASHI(2) , Kin’ya TAKAHASHI(1)(1) Department of Physics and Information Technology, Kyushu Institute of Technology, Japan, takahasi@phys.kyutech.ac.jp(2) Research Institute for Information Technology, Kyushu University, Japan, tkoba@cc.kyushu-u.ac.jp

ABSTRACTTwo and three-dimensional models of a test-tube thermoacoustic engine were numerically analyzed using compressible Large Eddy Simulation (LES) to investigate initial transient behavior, i.e., generation mechanism of
thermoacoustic waves in an initial state. In the model used in this study, a stack is placed near the bottom of
the test-tube and a temperature gradient is applied between both ends of the stack. The model has an external
region connecting the opening of the test-tube for radiations of sound waves and heat. As a result, a ﬂuid ﬂow
was observed inside the stack, a strong pressure oscillation, i.e., acoustic resonance, was observed inside thetest-tube, and sound radiation from the open end was also observed. Furthermore, the frequency of the soundvibration was almost the same as the theoretical estimation of the resonance frequency of the test-tube. Thus,
we successfully reproduced the basic properties of the thermoacoustic engine in the initial state. However, noise
components increased in time evolution and stationary oscillations were not attained yet. Thus, we need to
improve our numerical method. We are also planning to analyze sound waves’ generation mechanism taking
into account aeroacoustic theory, e.g., Lighthill’s acoustic analogy.

Keywords: Thermoacoustic, Stack, compressible LES

1

INTRODUCTION

Thermoacoustics is the interaction between thermodynamic phenomena and acoustic phenomena. A thermoacoustic phenomenon is typically observed when a gas column conﬁned in a long cylindrical tube is subjected
to strong temperature gradients[1]. Namely, heat and acoustic ﬁeld exchange energy due to ﬂuid oscillatory motion induced by a strong temperature gradient in a narrow channel so that a spontaneous oscillation with large
amplitude is sustained. Thermoacoustic phenomena and thermoacoustic engines have been received considerable
attentions for several hundred years [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]. The mechanism of
thermoacoustic phenomena has been investigated from the viewpoint of non-equilibrium thermodynamics combined with nonlinear ﬂuid dynamics. The basic properties of thermoacoustic phenomena have been gradually
elucidated from the viewpoints of thermodynamics and ﬂuid dynamics. However, there are many unsolved
problems because of the great complexities of thermoacoustic systems, and there are fewer publications fromthe viewpoint of aeroacoustics[17, 18]. Furthermore, numerical analysis of thermoacoustic phenomena is still ahard task because it requires a highly accurate numerical calculation of compressible ﬂuid motion under a strong
temperature gradient for a time interval that is long enough to attain stationary thermoacoustic oscillations[15].
From the viewpoint of engineering, various universities and companies have been researching on thermoacoustic engines, which utilize this phenomenon to operate engines and refrigeration units from waste heat ofautomobiles and factories [8, 12, 14]. Thermoacoustic engines have the advantages of being environmentallyfriendly and having no moving parts, but they also have problems such as extremely high operating temperatures and insufﬁcient efﬁciency.
In this paper, we consider a typical example of thermoacoustic phenomena, namely thermoacoustic oscillations observed when a test-tube ﬁlled with steel wool is heated at the bottom[8, 16]. Even for such a simple

situation, the mechanism of sound generation is not completely understood, yet. In this paper, we numericallystudied two and three-dimensional models of a test-tube thermoacoustic engine with compressible Large Eddy
Simulation (LES) to explore the generation mechanism of thermoacoustic waves in an initial transient interval.

2

MODEL AND NUMERICAL METHOD

In this paper, we studied three-dimensional (3D) and two-dimensional (2D) models of a test-tube with a compressible LES solver. Figure 1 shows the geometry of the 3D model. The test-tube model is of a rectangulartube, which is 150.0mm in length and has a cross section with a height of 21.2mm and a width of 9.2mm. The
stack is placed at a distance of 10mm from the bottom of the test-tube and is 30.0mm in length. The stackconsists of 11 × 5 square tubes, each of which has a square cross section with an area of 1.2 × 1.2mm2 andwhich are placed in an equidistance to each other by 0.8mm. The right rectangular parallelepiped represents anexterior domain with a volume of 123 × 246 × 246mm3 . Except for the left boundary of the exterior domain, atransparent condition, the Poinsot-Lele method, is imposed on the boundary walls, while the left boundary is asolid wall[19]. The geometry of the 2D model is the same as the cross section of the 3D model through thecenter line of it and parallel to the sheet (see Figure 1).
Hot and cold heat exchangers each with a length of 10mm are attached to left and right sides of the stack tocontrol the side wall temperatures, respectively. The temperature of the hot exchanger is increased from 300K
to 800K for the ﬁrst 0.002s and takes a constant value of 800K, while the temperature of the cold exchanger is
ﬁxed at 300K. Thermoacoustic energy conversion is essentially controlled by a parameter Y = ω r2 /2α , whereω is the angular frequency of acoustic oscillation, r is the characteristic transverse length of the channel, i.e.
radius, and α is the thermal diffusivity of gas[11, 12]. The wavelength of the fundamental mode is fourtimes the length of the test-tube. Thus, the resonance angular frequency ω of the test-tube is estimated as
ω = 2π c0 /4L ≈ 3644s−1 at the temperature T = 300K, where L is the length of the test-tube, the effective
radius of the square tube in the stack is estimated as r ≈ 0.677mm, and the thermal diffusivity of air is given
as α ≈ 117mm2 s−1 at T = 800K. Thus, the control parameter is given as Y ≈ 7.14, which is nearly 7 times
greater than the optimal value of Y ≈ 1. However, for convenience of numerical setup, we accept this parametervalue, even though thermoacoustic oscillation is less excitable.
For numerical calculation, we adopted a compressible Large-Eddy Simulation (LES) solver. Incompressible
LES, vortices larger than the grid size are directly calculated by the system of compressible ﬂuid equations,while the effect of vortices smaller than the grid size is estimated by using a statistical model (SGS model).
We selected a ’one-equation eddy’ model as the SGS model. Practically, we used rhoPimpleFoam with the
SGS model ’one-equation eddy’ in OpenFOAM, a solver for subsonic and lower ﬂow velocities. Table 1 showsparameters of the models. For the ’3D model’, the minimum grid size is taken as ∆l = 0.1mm. For 2D
calculations, we take two models, which are different in the minimum grid size: a normal mesh model ’2Dmodel’ with ∆l = 0.1mm and a ﬁner mesh model ’2D model f’ with ∆l = 0.05mm. The time step for allmodels is taken as ∆t = 5 × 10−8 s. For the 3D model, time evolution up to 0.018sec is calculated, while forthe 2D models, it is calculated up to 0.1sec. Figure 1 (b) also shows observation points of dynamical variables,
which are located on the center line. Table 2 shows the positions of the observation points.
Table 1. Parametets of models
Modelpoints

cells

faces

minimum grid ∆l [mm]calculation time [s]3D Model86602917

85328544

257242144

0.1

0.018

2D Model840682415032

1665446

0.1

0.1

2D Model f

33415101660128

6651148

0.05

0.1

(a)

(b)

(c)

(d)

Figure 1. 3D Model of a test-tube. (a) 3D bird’s-eye view. (b) 2D central cross-section with observation points.
(c) Enlarged drawing of the stack on 2D center cross-section. (d) Vertical cross-section of the stack.

Table 2. Distances of observation points from the bottom of the test-tube.

3

Observation point

p1

p2

p3

p4

Distance [mm]

5

25

140

210

NUMERICAL RESULTS

3.1 3D model
Figure 2 (a) and (b) show the pressure and velocity distributions at t = 0.012s, respectively. A strong acoustic oscillation is observed inside the test-tube and an acoustic wave with a smaller amplitude is radiated fromthe open end to the exterior domain. Figure 3 shows pressure ﬂuctuations at the observation points and their
Fourier spectra. At the point p1 in the hot exchanger and the point p2 in the stack, strong oscillations of
the fundamental mode are observed, but high frequency noise components are superposed on them and grow intime evolution. From the Fourier spectra, the dominant peaks of the fundamental frequency are observed around
600Hz and subdominant ones corresponding to the third harmonic exist around 1800Hz. The fundamental frequency f ≈ 600Hz is very close to the theoretical estimation at f ≈ 580Hz at T = 300K. Thus, the oscillationof the fundamental mode is excited, though it is accompanied by noise components. At the point p3 near the
open end of the test-tube, the amplitude of the oscillation becomes smaller, since standing waves of pressure
have nodes at the open end. Though, the oscillation is more and more inﬂuenced by noise in time evolution,
the peak of the fundamental frequency is still dominant in the Fourier spectrum. At the point p4 in the exteriordomain, the oscillation becomes smaller in amplitude and the inﬂuence of noise increases in time evolution, but
the fundamental frequency is still dominant in the Fourier spectrum.
(a)

(b)

Figure 2. Pressure and velocity distributions at t = 0.012s. (a) Pressure. The scale of the color bar in Pa. (b)Velocity. The scale of the color bar in m/s.
Figure 4 shows velocity ﬂuctuations at the observation points and their Fourier spectra. At the point p1, due
to the boundary condition of velocity at solid walls, the oscillation of velocity takes small values in amplitude
and is disturbed by noise with a small amplitude. On the other hand, at the point p3, a clear oscillation of
the fundamental mode is observed with fewer noise components, though its amplitude slightly decays in time
evolution. At the point p2 in a narrow channel of the stack, absolute values of velocity become large due to thevolume ﬂow conservation. First, a mean ﬂow toward the right is excited due to an increase in the temperaturein the hot exchanger and the magnitude of velocity increases, but it decays oscillating with frequencies around
600Hz and being disturbed by high frequency noises in time evolution. At the point p4, the oscillation becomes
smaller in amplitude and the inﬂuence of noise increases in time evolution. For all observation points, thefundamental frequency is dominant in the Fourier spectra.
Figure 5 shows temperature ﬂuctuations at the points p1 and p2. The temperatures do not increase but rather
ﬂuctuate irregularly, though they increase in an initial short time interval. Actually, the whole volume of the hot
exchanger can not be heated in this short time simulation. Even though a sudden increment of the temperatureon the walls of the hot exchanger initiates thermoacoustic oscillations, the temperature gradient in the stack is
not large enough to sustain an acoustic oscillation excited in the test-tube; thus, it decays in time evolution
probably until the temperature reaches a value high enough.

(a)

(b)
100

p

fourierp

10020010p [pa]

p [Pa]

100100100000

99900

1

0.1

99800
0

0.002 0.004 0.006 0.008

0.01

0.01

0.012 0.014 0.016 0.018

0

1000

2000

Time [sec]

3000

4000

5000

f [Hz]

(c)

(d)
100

p

fourierp

10020010p [pa]

p [Pa]

100100100000

99900

1

0.1

99800
0

0.002 0.004 0.006 0.008

0.01

0.01

0.012 0.014 0.016 0.018

0

1000

2000

Time [sec]

3000

4000

5000

f [Hz]

(e)

(f)
100

p

fourierp

10020010p [pa]

p [Pa]

100100100000

99900

1

0.1

99800
0

0.002 0.004 0.006 0.008

0.01

0.01

0.012 0.014 0.016 0.018

0

1000

2000

Time [sec]

3000

4000

5000

f [Hz](g)(h)
10000210pfourierp

100002
100001

1

p [pa]

p [Pa]

1000001000000.1

99999.5
99999

0.01

99998.599998

00.002 0.004 0.006 0.008

0.01Time [sec]0.012 0.014 0.016 0.018

0.001

0

1000

2000

3000

4000

5000

f [Hz]

Figure 3. Pressure ﬂuctuations at the observation points and Fourier spectra. (a) Pressure ﬂuctuation at the point
p1. (b) Frequency spectrum at the point p1. (c) Pressure ﬂuctuation at the point p2. (d) Frequency spectrumat the point p2. (e) Pressure ﬂuctuation at the point p3. (f) Frequency spectrum at the point p3. (g) Pressure
ﬂuctuation at the point p4. (h) Frequency spectrum at the point p4.

(a)

(b)
1

U

1.5

0.1

1

0.01

U [m/s]U [m/s]

2

0.5

0.001

0

0.0001-0.5

fourierU

1e-05
0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0

1000

2000

Time [sec]

3000

4000

5000

f [Hz]

(c)

(d)
1

U

1.5

0.1

1

0.01

U [m/s]U [m/s]

2

0.5

0.001

0

0.0001-0.5

fourierU

1e-05
0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0

1000

2000

Time [sec]

3000

4000

5000

f [Hz]

(e)

(f)
1

U

1.5

0.1

1

0.01

U [m/s]U [m/s]

2

0.5

0.001

0

0.0001-0.5

fourierU

1e-05
0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0

1000

2000

Time [sec]

3000

4000

5000

f [Hz]

(g)

(h)
0.1

U

0.006

0.01

0.004

0.002

U [m/s]U [m/s]fourierU00.001

0.0001-0.0021e-05-0.0041e-06
00.002 0.004 0.006 0.008

0.01Time [sec]0.012 0.014 0.016 0.018

0

1000

2000

3000

4000

5000

f [Hz]

Figure 4. Velocity ﬂuctuations at the observation points and Fourier spectra. (a) Velocity ﬂuctuation at the point
p1. (b) Frequency spectrum at the point p1. (c) Velocity ﬂuctuation at the point p2. (d) Frequency spectrumat the point p2. (e) Velocity ﬂuctuation at the point p3. (f) Frequency spectrum at the point p3. (g) Velocity
ﬂuctuation at the point p4. (h) Frequency spectrum at the point p4.

(a)

(b)
302

T

301.5

301.5

301

301
T [K]

T [K]

302

300.5

300.5

300

300

299.5

299.5

299

0

0.002 0.004 0.006 0.008

0.01Time [sec]0.012 0.014 0.016 0.018

T

299

0

0.002 0.004 0.006 0.008

0.01

0.012 0.014 0.016 0.018

Time [sec]Figure 5. Temperature ﬂuctuations in the hot exchanger and stack. (a) Temperature ﬂuctuation at the point p1.
(b) Temperature ﬂuctuation at the point p2.
3.2 2D model
Figure 6 shows pressure ﬂuctuations at the observation points and their Fourier spectra for the ’2D model’, andFigure 7 shows those for the ’2D model f’. For both models, in an initial interval up to 0.01s, oscillations of
the fundamental mode are observed at all the observation points, but irregular ﬂuctuations take place of themin a short time. However, for both models, the peaks of the fundamental mode are still dominant in Fourier
spectra. The oscillations of the fundamental mode in the initial stage are smaller than those for the ’3D model’.
This is because a weaker reﬂectance at the 2D open end of a pipe compared with that at the 3D open end
reduces standing waves in amplitude[20]. The irregular oscillations for the ’2D model’ are larger in amplitude
than those for the ’2D model f’. Thus, the appearance of irregular oscillations may be possibly attributed to theless accuracy of numerical simulations.
Figure 8 shows temperature ﬂuctuations at the points p1 and p2 for the ’2D model’ and ’2D model f’.
For both models, the temperatures increase at the point p1, while they ﬂuctuate irregularly at the point p2.
Since the increments of the temperature are only 333K and 335K for the two models, the temperatures in the
hot exchanger are not still high enough to make temperature gradients in the stack and to sustain stationary
acoustic oscillations in the test-tube.

4

CONCLUSIONS

To investigate the initial transient behavior of a test-tube thermoacoustic engine, two and three-dimensionalmodels were numerically studied using a compressible Large Eddy Simulation (LES) scheme. As a result,strong ﬂuid ﬂows, which are changed periodically, and large pressure oscillations of the fundamental mode
were observed inside the test-tube and acoustic waves radiated from the open end were also observed. In thissense, our simulations successfully reproduced basic properties of the thermoacoustic engine.
However, after the initial transient states, the periodic oscillations were replaced by high frequency irregularoscillations in a short time. The reasons are as follows. The air in the hot exchanger was not heated enough toform a stationary temperature gradient in the stack and to sustain standing waves in the test-tube. Furthermore,
the control parameter of the thermoacoustic engine Y = ω r2 /2α ≈ 7.14 was nearly 7 times greater than the
optimal value of ω r2 /2α ≈ 1, and the calculation times, 0.018s for the 3D model and 0.1s for the 2D models,
were too short to excite stationary acoustic oscillations in the test-tube, because it normally spends several tensof seconds and more to grow standing waves in the test-tube[16].
There are several ways to improve our simulations. First, we need to set the control parameter at the optimalvalues as ω r2 /2α ≈ 1. To do this, for example, the cross-section of the square tubes of the stack, which is
proportional to r2 , should be reduced and/or the length of the test-tube should be taken longer to reduce theangular frequency ω . The former requires a smaller grid size to reproduce ﬂows inside narrow channels of
the stack correctly thereby increasing the total number of cells, and the latter also increases the total number of

(a)

(b)
10010010p1p [pa]

p [Pa]

100050100000

99950

99900

fourierp

0.1

0.01

0

0.02

0.04

0.06

0.08

0.001

0.1

0

500

1000

1500

Time [sec]

2000

2500

3000

3500

4000

f [Hz](c)(d)
10010010p1p [pa]

p [Pa]

100050100000

99950

99900

fourierp

0.1

0.01

0

0.02

0.04

0.06

0.08

0.001

0.1

0

500

1000

1500

Time [sec]

2000

2500

3000

3500

4000

f [Hz](e)(f)
10004010pfourierp

1000301000201

p [pa]

p [Pa]

100010100000

0.1

99990
99980

0.01

99970
99960

0

0.02

0.04

0.06

0.08

0.001

0.1

0

500

1000

1500

Time [sec]

2000

2500

3000

3500

4000

f [Hz](g)(h)
10001010p1p [pa]

p [Pa]

100005

100000

99995

99990

fourierp

0.1

0.01

0

0.02

0.04

0.06

Time [sec]

0.08

0.1

0.001

0

500

1000

1500

2000

2500

3000

3500

4000

f [Hz]

Figure 6. Pressure measurement results. (a) Pressure-time distribution at p1. (b) Frequency analysis of pressure
at p1. (c) Pressure-time distribution at p2. (d) Frequency analysis of pressure at p2. (e) Pressure-time distribution at p3. (f) Frequency analysis of pressure at p3. (g) Pressure-time distribution at p4. (h) Frequency analysis
of pressure at p4.

(a)

(b)
10010010p1p [pa]

p [Pa]

100050100000

99950

99900

fourierp

0.1

0.01

0

0.02

0.04

0.06

0.08

0.001

0.1

0

500

1000

1500

Time [sec]

2000

2500

3000

3500

4000

f [Hz](c)(d)
10010010p1p [pa]

p [Pa]

100050100000

99950

99900

fourierp

0.1

0.01

0

0.02

0.04

0.06

0.08

0.001

0.1

0

500

1000

1500

Time [sec]

2000

2500

3000

3500

4000

f [Hz](e)(f)
10004010pfourierp

1000301000201

p [pa]

p [Pa]

100010100000

0.1

99990
99980

0.01

99970
99960

0

0.02

0.04

0.06

0.08

0.001

0.1

0

500

1000

1500

Time [sec]

2000

2500

3000

3500

4000

f [Hz](g)(h)
1000101p

0.1

p [pa]

p [Pa]

100005

100000

99995

99990

fourierp

0.01

0.001

0

0.02

0.04

0.06

Time [sec]

0.08

0.1

0.0001

0

500

1000

1500

2000

2500

3000

3500

4000

f [Hz]

Figure 7. Pressure measurement results. (a) Pressure-time distribution at p1. (b) Frequency analysis of pressure
at p1. (c) Pressure-time distribution at p2. (d) Frequency analysis of pressure at p2. (e) Pressure-time distribution at p3. (f) Frequency analysis of pressure at p3. (g) Pressure-time distribution at p4. (h) Frequency analysis
of pressure at p4.

(a)

(b)
340

2D
2Df

2D
2Df

300.4

330
300.2

T [K]

T [K]

320
300

310
299.8
300
299.6
290

0

0.02

0.04

0.06

Time [sec]

0.08

0.1

0

0.02

0.04

0.06

0.08

0.1

Time [sec]Figure 8. Temperature ﬂuctuations in the hot exchanger and stack for the ’2D model’ and ’2D model f’. (a)Temperature ﬂuctuation at the point p1. (b) Temperature ﬂuctuation at the point p2.
cells. Thus, the numerical cost is more expensive for performing both improving methods. Second, to reproduce
stationary oscillations, we need to take the calculation time long enough, but it requires a huge numerical cost.
Actually, the expected calculation time is approximately several hundred times as long as the present one. Thus,
this plane is not realistic To solve this difﬁculty, one takes the initial values of dynamical variables to mimic
those in a stationary state, in which standing waves are sustained in the test-tube. For example, the initial
distribution of the temperature is set such that it takes values of 800K for the air in the hot exchanger and
300 for the other parts except for the hot exchanger, and the temperature gradient in the stack is given tocontinuously connect it between the hot and cold exchangers. To investigate the energy transition mechanism
between thermoﬂuid and acoustic oscillation, we need the analysis considering the relation to the aeroacoustic
theory, e.g. Lighthill’s analogy including the second and third source terms regarded as thermoacoustic sources.

ACKNOWLEDGEMENTS
The present work was supported by Grant-in-Aid for Scientiﬁc Research (C) Nos. 19K03655 from the JapanSociety for the Promotion of Science (JSPS) and Joint Usage/Research Center for Interdisciplinary Large-Scale
Information Infrastructures and High Performance Computing Infrastructure in Japan (Project ID: jh220001).

REFERENCES[1] Taconis KW, Beenakker JJM, Nier AOC, Aldrich LT. Measurements concerning the vapour-liquid equilibrium of solutions of He in He below 2.19 ° K. Physica 15: 1949; 733-739.
[2] Feldman KT. Review of the literature on Rijke thermoacoustic phenomena. J. Sound. 1968; 7: 83.
[3] Rott N. Thermally driven acoustic oscillations. part 2: Stability limit for helium. Z. Angew Math. Phys.
1973; 24: 54-72.
[4] Rott N. Thermoacoustics. Advances in Applied Mechanics. 1980; 20: 135-175.
[5] Ceperley PH. A pistonless Stirling engine–The traveling wave heat engine. J. Acoust. Soc. Am. 1979; 66:
1508-1513.
[6] Ceperley PH. Gain and efﬁciency of a short traveling wave heat engine. J. Acoust. Soc. Am. 1985; 77:1239-1244.
[7] Wheatley J, Holfer T, Swift GW, Migliori A. Understanding some simple phenomena in thermoacoustics
with applications to acoustical heat engines. Am. J. Phys. 1985; 53: 147-162.

[8] Swift GW. Thermoacoustic engines. J. Acoust. Soc, Am. 1988; 84: 1145-1180.
[9] Dowling AP. The Calculation of Thermoacoustic Oscillations. J. Sound. Vib. 1995; 180: 557-581.
[10] Tominaga A. Thermodynamic aspects of thermoacoustic theory. Cryogenics. 1995; 35: 427-440.
[11] Yazaki T. Experimental observation oftherrnoacoustic turbulence and universal properties at the quasiperiodic transition to chaos. Phys Rev E. 1993; 48: 1806-1818.
[12] Yazaki T, Iwata A, Maekawa T, Tominaga A. Traveling Wave Thermoacoustic Engine in a Looped Tube.
Phys Rev Lett. 1998; 81: 3128-3131.
[13] Berson A, Blanc-Benon P. Nonperiodicity of the ﬂow within the gap of a thermoacoustic couple at highamplitudes. J Acoust Soc Am. 2007; 122: 122-127.
[14] de Waele ATAM. Basic Operation of Cryocoolers and Related Thermal Machines J. Low Temp. Phys.
2011; 164: 179-236.
[15] Ishii K, Kitagawa S, IshigakiM, Adachi S. Vortical ﬂow structure of thermoacoustic oscillations in a closed
tube. Fluid Dyn. Res. 2014; 46: 061408.
[16] Olivier C, Poignand G. Pénelet G Do it yourself: make your own thermoacoustic engine with steel woolor rice. Eur. J. Phys. 2017; 38: 015101.
[17] Lighthill MJ. On sound generated aerodynamically. Part i: General theory. Proc. Roy. Soc. London A.
1952; 211: 564-587.
[18] Howe MS. Acoustics of ﬂuid-structure interactions. Cambridge Univ. Press; 1998.
[19] Poinsot TJ, Lelef SK. Boundary conditions for direct simulations of compressible viscous ﬂows. J Comp
Phys. 1992; 101: 104-129.
[20] Miyamoto M, et al. Numerical study on acoustic oscillations of 2D and 3D ﬂue organ pipe like instrumentswith compressible LES.

ABS-0251

Numerical study of the feedback mechanism of the edge tone
Tatsuki ONOMATA(1) , Sho IWAGAMI(1) , Ryoya TABATA(1) , Taijiro OHNO(1) , Takeshi NANRI(2) , Taizo KABAYASHI(2) ,Kin’ya TAKAHASHI(1)(1) Kyushu Institute of Technology, Japan, takahasi@phys.kyutech.ac.jp(2) Kyushu University, Japan, tkoba@cc.kyushu-u.ac.jp

ABSTRACT
We numerically investigate fundamental problems of the edge tone with compressible Large Eddy Simulation (LES)
together with acoustic solver FDTD and incompressible LES. Jet oscillation and edge tone in the first mode aresuccessfully reproduced by a 3D model with compressible LES. Namely, the acoustic intensity changes with the jet
velocity well following the sixth power law, which is an evidence of the reliability of our numerical method. Next, weestimate the intensity of acoustic feedback in the following way. According to Kaykayoglu and Rockwell, effective
pressure sources are considered to be located slightly downstream of the edge tip on both sides of the edge. Indeed,such a pair of positive and negative pressure spots periodically appear in our numerical calculation. Then, we set thepressure spots on both sides of the edge and reproduce acoustic waves radiated from them by FDTD. The acoustic
particle velocity of the reproduced acoustic field at the nozzle outlet is regarded as acoustic feedback. Even thoughsuch acoustic feedback may make a contribution to driving the jet, we can consider that the fluid feedback is still
dominant in a low-Reynolds number regime as pointed out by Paál et al. from the results of incompressible LES.

Keywords: Edge tone, Aerodynamic sound, Air-jet instrument, LES

1

INTRODUCTION

The edge tone is a type of aerodynamic sound observed in the low Mach range [1, 2]. When a thin jet emanatedfrom a nozzle is directed to a wedge-shaped edge, a spontaneous vibration of the jet occurs and the unsteadymotion of the fluid produces an edge tone[2, 3, 4]. The generation mechanism of the edge tone has not been
fully understood, and is still an important subject in the field of aeroacoustics, [3, 4, 5, 6, 7, 8, 9] and also in
the field of musical acoustics, because the edge tone is sound sources of air-jet instruments, e.g. recorder, fluteand organ pipe [10, 11, 12, 13].
In the long history of the study of the edge tone, important phenomenological formulae have been proposed
to describe the basic properties of the edge tone by many authors. Brown found that the frequency of the edge
tone increases linearly with the jet velocity until a mode transition occurs[3]. At a mode transition, the edge
tone abruptly changes in frequency when the hydrodynamic wave of the jet discontinuously changes to a higher
mode wave with change of a control parameter, e.g. the jet velocity. Such a mode transition is hysterical:
upward and downward transitions follow different paths. The basic properties and sound generation mechanismof the edge tone have been studied by Powell and subsequent authors [4, 5, 6, 7, 8, 9]. Powell found that thesound intensity of the edge tone obeys the sixth power of the jet velocity, namely the sixth power law, which isan evidence of the dipole-like radiation of the edge tone[4]. As also pointed out by Powell[4], the jet oscillation
is sustained by a feedback cycle, which is induced by the interaction of the jet with the edge. Therefore, thestudy of the feedback mechanism is a very important subject to achieve a comprehensive understanding of theedge tone. However, the feedback mechanism is not understood completely. Crighton and Paál et al. claimed
that the feedback mechanism can be explained as an incompressible fluid process [8, 9, 14]. On the other hand,
Kaykayoglu and Rockwell indicated that a pair of effective pressure sources are located slightly downstream ofthe edge tip on both sides of the edge plate [6, 7]. Such pressure sources should induce acoustic feedback.

In this paper, we numerically study the basic properties and feedback mechanism of the edge tone with 3D
compressible Large Eddy Simulation (LES), because some reliable numerical results on the edge tone have beenreported[14, 15, 16, 17]. First, to confirm the reliability of the simulation, we reproduce the relationship between
the jet velocity and sound frequency, i.e., Brown’s equation, and the relationship between the jet velocity andsound intensity, i.e., the sixth power law. Then, we explore the feedback mechanism and consider the problemof which feedback process, fluid or acoustic feedback, dominates the feedback cycle with comparing the resultof the compressible LES with those of an incompressible LES and an acoustic simulation by using FDTD. In
the acoustic simulation, we consider the acoustic feedback induced by the effective pressure sources introduced
by Kaykayoglu and Rockwell [6, 7].

2BASIC FEATURES OF EDGE TONE

In this section, the basic features of the edge tone are reviewed. As shown in Figure 1, a jet emitted from a
nozzle collides with an edge, generating vortices and sound. This interaction with the edge induces feedback
towards the nozzle outlet and influences the jet to oscillate in the vertical direction. This feedback process
makes a cycle of events, which is periodically repeated to sustain the jet oscillation[4].
The relationship between the oscillation frequency of the edge tone and the jet velocity was obtained experimentally by Brown, i.e., Brown’s equation[3]f = 0.466 j(100U − 40)(1/100l − 0.07),(1)

where f [Hz], U [m/s] and l [m] are the oscillation frequency, jet velocity and distance between the nozzle
outlet and the edge, i.e., stand-off distance, respectively. Since the variables of f , U and l are in SI units, thetwo constants with units are 40 m/s and 0.07m−1 , while the other constants are dimensionless. The parameterj changes depending on the oscillation mode of the jet and takes values j = 1.0, 2.3, 3.8 and 5.4. The valuej = 1.0 corresponds to the first hydrodynamic mode and the other values correspond to higher hydrodynamic
modes. As shown in Figure 2, a mode transition is always hysteretic.
Powell found the relationship between the jet velocity and sound intensity: it follows the sixth power of jet
velocity as a dipole radiation[4]. He also stated that the sound radiation of edge tones is strongly directed in
the vertical direction.

Figure 1. Feedback process in the edge tone.

Figure 2. Mode transition of the edge tone

3

MODEL AND NUMERICAL METHOD

3.1 Model and numerical method
Figure 3 (a) and (b) show the 3D model of the edge tone studied in this paper. The dimensions of the model
are taken as l = 5mm, Lnozzle = 5mm, Ledge = 3mm, L = 22mm, d = 1mm, wnozzle = 2mm, znozzle = 24mm. The
distance between the nozzle and the tip of the edge and the height of the nozzle are respectively taken as l = 5mm and d = 1 mm. The ratio l/d = 5 is a typical value for air-jet instruments[10, 12]. In Figure 3 (a), thepoint indicated by a bullet at the distance of xo =4mm from the nozzle outlet is an observation point of velocity.
The ears indicated by the label ’Guide’ in Figure 3 (b) hold a flow channel between the edge plate and nozzle,
and prevent the jet from deviating from the channel.
(a)

(b)

Figure 3. Numerical model of the Edge tone. (a) 2D central cross-section. (b) 3D bird’s-eye view.
3.2 Compressible analysis and Numerical scheme
The edge tone is caused by the complex interaction between fluid and sound. Therefore, a compressible fluid
solver is necessary to reproduce the edge tone accurately. In this study, a Large-Eddy Simulation (LES) solver
is used for calculations. In LES, vortices larger than the grid size are directly calculated by the Navier-Stokes
equations, while the effect of vortices smaller than the grid size are estimated by using a statistical model (SGSmodel). We selected a one-equation eddy model as the SGS model. Practically, we used OpenFOAM (Opensource Field Operation And Manipulation), which is an open source Computational Fluid Dynamics (CFD)
toolbox available under the GNU General Public License (GPL). Several types of compressible LES solvers areavailable in OpenFOAM, and we chose rhoPimpleFoam, a solver for subsonic and lower flow velocities.

3.3 Numerical mesh
Figure 4 schematically shows the structure of the numerical mesh. To reduce the number of cells, we havedeveloped the method called “spider mesh”. That is, for the core part, in which the nozzle and edge plate
are embedded, finer grids are used, while the peripheral part, which is less important for calculations, is continuously stretched and expanded outward like a spider web. The dimensions of the core part were set as
24 × 24 × 36mm3 in order to reproduce the fluid and acoustic motions of interest.

Figure 4. Structure of the Numerical Mesh
3.4 Incompressible Analysis
Paál et al. showed that hydrodynamic oscillations of the jet and mode transitions among them can be reproduced
by an incompressible fluid solver, though true sound radiation is not reproduced [14]. This fact implies that amajor part of the feedback is constructed by components of the incompressible fluid [8, 9]. In this paper,
we implemented incompressible fluid simulations to estimate, through comparison with results of compressible
fluid simulations, to what extent the feedback is attributed to an incompressible fluid process. For practical
calculations, we used LES with the SGS model ’one-equation eddy’ adopting PimpleFoam in OpenFOAM, anincompressible fluid solver.
3.5 Acoustic simulation
Kaykayoglu and Rockwell suggested that a pair of pressure spots with opposite signs to each other periodicallyappear slightly downstream of the edge tip on both sides of the edge plate and may act as a dipole soundsource[6, 7]. To estimate acoustic feedback from such a dipole-like source, we implemented acoustic simulations
with a Finite-difference time-domain method(FDTD). Due to our numerical ability, we treated a 2D model.
Actually, we calculate the following system of equations with FDTD,∂v= −∇p,
∂t
1 ∂p
−
= ∇v,
κ ∂t

(2)

ρ0

(3)

where v and p denote the acoustic particle velocity and acoustic pressure, and ρ0 and κ are the air density at
rest and the volume modulus, respectively. We set as ρ0 = 1.205[kg·m−2 ] and κ = ρ0 ·c0 ·c0 = 142, 180[Pa] Table
1 shows parameters of numerical calculations with the three solvers.
Table 1. Parameters of numerical calculations with three solvers
Solver

Minimum grid size [mm]Number of grids

Caluculate region [mm]Time step [s]Compressible

0.1108798947

168 × 168 × 248

1.0 × 10−7

Incompressible

0.1108798947

168 × 168 × 248

5.0 × 10−6

FDTD

0.05

100000000

50 × 50

1.0 × 10−7

4

NUMERICAL RESULT

4.1 Velocity and pressure oscillations obtained with compressible LES
To confirm the reliability of the numerical simulation, we check the basic properties of jet oscillations andthose of acoustic oscillations obtained with the compressible LES. Figures 5 (a) and (b) show the velocity
and pressure distributions at U = 10.0 m/s, respectively. As shown in 5 (a), a well-sustained jet oscillation
is observed. As shown in 5 (b), the pressure distribution is antisymmetric with respect to the edge plate. As
pointed out by Kaykayoglu and Rockwell[6, 7], a pair of pressure spots with opposite signs is observed on bothsides of the edge plate and seems to work as effective sound sources, which radiate sound waves in anti-phases
into the upper and lower half planes. Thus, the sound field is similar to that generated by a dipole source.
Figures 6 (a)-(f) show changes of the vertical velocity of the jet in the range from U = 6 to 20 m/s.
Figure 7 shows the comparison in frequency between Brown’s equation and numerical results in Figure 6,
where the blue and green lines indicate the first and second modes of Brown’s equation, respectively. As
shown in Figure 6, the jet motion reaches a stationary oscillation at each jet velocity. Actually, in the range
6 ≤ U ≤ 15m/s, oscillations of the first mode are observed and the amplitude of the vertical velocity increases
with the jet velocity. According to Brown’s experiment[3], at l = 5mm, the first mode was observed in the range
6 ≤ U < 12m/s, a hysteretic mode transition was observed in the range 12 ≤ U ≤ 17.5m/s, and the second mode
was observed in the range U > 17.5m/s. At U = 20m/s, a complex oscillation like a second mode is observedat the beginning but finally changes to an oscillation of the first mode. Actually, the frequencies corresponding
to the first and second modes are observed in the Fourier decomposition. Thus, our numerical simulation seems
to be less accurate in the second mode regime.
Figure 8 shows the vorticity distribution visualized by using a volume rendering of Q-criterion at U=10m/s[13].
In the interval between the nozzle and edge, vortex sheets held by the ears are observed, namely the vorticity
distribution of the wavy jet. Therefore, the ears are necessary to sustain a regular oscillation of the jet. In theregions above and below the edge, cylindrical vortices created by the collision with the edge are observed andshould contribute to feedback towards the nozzle outlet. In regions far from the tip of the edge, the vortices
however break into small pieces and irregular distributions of vorticity are observed.
(a)

(b)

Figure 5. Distirbutions of physical quantities on the central section at t=0.03524s and at U=10m/s (a) Velocity
profile. (b) Pressure profile.

(a)

(b)
3

U

2

2

1

1
U [m/s]U [m/s]

3

0

0

-1

-1

-2

-2

-3

0

0.01

0.02

0.03

0.04

0.05

-3

0.06

U

0

0.005

0.01

Time [sec]

0.015

0.02

0.025

0.03

0.035

Time [sec]

(c)

(d)
4

U

3

3

2

2

1

1
U [m/s]U [m/s]

4

0

0

-1

-1

-2

-2

-3

-3

-4

0

0.005

0.01

0.015

0.02

0.025

0.03

-4

0.035

U

0

0.005

Time [sec]

0.01

0.015

0.02

0.025

Time [sec]

(e)

(f)
6

U

U

4
4

2
U [m/s]U [m/s]

2

0

0

-2

-2

-4
-4
0

0.005

0.01
Time [sec]

0.015

0.02

-6

0

0.005

0.01

0.015

0.02

Time [sec]Figure 6. Changes of vertical velocity at the observation point in Figure 3. (a) for representative values of
the jet velocity. (a) Oscillation at U = 6m/s. (b) Oscillation at U = 8m/s. (c) Oscillation at U = 10m/s. (d)Oscillation at U = 12m/s. (e) Oscillation at U = 15m/s. (f) Oscillation at U = 20m/s.

4500First mode of Brown's eq
Second mode of Brown's eq
First mode
Second mode

4000
3500

f [Hz]

3000
2500
2000
1500
1000
500
0
2

4

6

8

10

12

14

16

18

20

U [m/s]Figure 7. Brownformula vs Numericalresult

Figure 8. Volume rendering of Q-criterion at t=0.028s and at U=10m/s.
4.2 Directivity of sound waves
To investigate the directivity of sound waves radiated, observation points were set on a circle with its center at
the middle point between the nozzle and edge and with a radius of 82mm (see Figure 9 (a)), and the soundintensity is defined by
1 2
I=
p ,
(4)
ρ0 c0 awhere pa is the amplitude of the sound pressure fluctuation at each observation point under a steady state
condition. Figure 9 (b) shows the distributions of the sound intensity in a logarithmic scale for the representativevalues of U. For every case, the sound intensity takes the maximum values in the vertical direction, which isin good agreement with the experimental results by Powell [4]. At each observation point, the sound intensity
increases with U.

(a)

(b)

Figure 9. Directivity of sound waves. (a) Observation points (b) Distributions of the sound intensity at theobservation points for the representative value of U.
4.3 Sound intensity
In this subsection, we explore the change of sound intensity I with the jet velocity U. To do this, we define
the total sound intensity as the sum of the values of I at the observation points on the circle (see Figure 9 (a)).
In Figure 10, the total sound intensities at the representative values of the jet velocity are compared with a lineof the sixth power law[4], which is adjusted to take the same value as the sound intensity at U = 6m/s. The
total sound intensity increases almost following 5.4-th power of the jet velocity U. Then, we consider that thisresult well reproduces Powell’s experiment, namely the sixth power law.

Figure 10. Sound intensity vs. 6th power law.

4.4 Estimation of feedback intensity
The jet oscillation should be sustained by fluid feedback from vortices and/or acoustic feedback from the effective sound source near the edge. Such feedback act as upward and downward velocities on the upstream
jet flow near the nozzle outlet, and the observation of vertical velocities at points just above and below the
upstream jet should provide an indirect measure of the feedback intensity: Figure 11 shows the observation
points U1 and U2 , which are on a vertical line 0.1mm downstream from the nozzle outlet, and 0.5mm upwardand downward from the center line of the nozzle, respectively. Figure 12 (a) and (b) show changes of verticalvelocities observed at the points U1 and U2 , with the compressible and incompressible simulations at U=12m/s,
respectively. As pointed out by Paál et al., the jet oscillations are well reproduced at the representative values ofU with the incompressible LES. However, the amplitude of vertical velocity fluctuations and their mean values
obtained at the point U1 and U2 with the incompressible LES are each slightly smaller than the corresponding
ones obtained with the compressible LES. Therefore, the feedback in the compressible simulation is stronger
than that in the incompressible simulation, and the discrepancy between them may be attributed to acoustic
feedback.

Figure 11. Feedback to the upstream region: U1 and U2 are observation points of vertical velocities.
(a)

(b)

Figure 12. Changes of the vertical velocities at the points U1 and U2 at U=12m/s. (a) Result of the compressible
simulation. (b) Result of incompressible simulation.
4.5 Estimate of acoustic feedback with FDTD
To estimate the strength of acoustic feedback, we implemented an acoustic simulation with FDTD. For convenience of simulation, we adopted a simplified 2D model (see Figure 13 (b)). As shown in Figure 13 (a), thestrength of the dipole sources can be estimated from the result of the compressible LES simulation. For simplicity, we assumed that dipole sources consist of a pair of fixed point sources with opposite signs (see Figure
13 (b)), and their values change as Gaussian functions:(C1 exp(a(t − t0 ))2
0 < t ≤ 2t0 ,p1 (t) =(5)
2
C2 exp(a(t − 3.0t0 )) 2t0 < t ≤ 4t0 ,(C2 exp(a(t − t0 ))2
0 < t ≤ 2t0 ,p2 (t) =(6)
2
C1 exp(a(t − 3.0t0 )) 2t0 < t ≤ 4t0 ,where the parameters C1 , C2 , t0 and ”a” were fitted in reference to the dipole-like pressure distributions aboveand below the edge observed in the LES. Table 2 shows values of the parameters.
Figure 13 (b) shows a dipole radiation reproduced by FDTD. Figure 14 shows the change of vertical acoustic
particle velocity vy at the observation point which is 0.1mm downstream from the nozzle and indicated bya bullet "•" in Figure 13(b). Apparently, acoustic feedback is reproduced, however the maximum values of
acoustic particle velocity, which are of nearly 2.36m/s, are much stronger than the vertical velocities in Figure
12. This is probably because the pressure spots mostly form the fluid pressure of the solenoidal velocity field
and a tiny part of them is spent for acoustic feedback. Also, this is partially due to the difference between the
2D and 3D systems. In either case, to estimate acoustic feedback correctly, one should treat Lighthill’s source
in a very precise and careful manner near the edge, because it provides not only sound sources but also sourcesof local pseudo sound pressure (or hydrodynamic pressure).
Table 2. Parameters of Gaussian functions(a)parameters

C1 [m3 s−1 ]C2 [m3 s−1 ]a [s−1 ]t0 [s]

values

8.0 × 10−2

−8.0 × 10−2

2.0 × 106

3.0 × 10−3(b)Figure 13. Estimation of acoustic feedback (a)Dipole sources observed in the compressible LES simulation at
U=12m/s. (b) Dipole radiation reproduced by FDTD.

Figure 14. Acoustic particle velocities observed at the point 0.1mm downstream from the nozzle outlet.

5

CONCLUSIONSThe 3D model calculated with the compressible LES accurately reproduced the fundamental properties of thefirst mode of the edge tone. That is, the frequencies of the jet oscillation well follow the first mode of Brown’s
equation, and the sound intensity almost obeys the sixth power law. Furthermore, the 3D simulations are moreaccurate in frequency than the previous 2D simulations performed with the same compressible LES [16]. Indeed,
the frequencies obtained with the 2D simulations slightly deviated from Brown’s equation even in the first mode
region. This is partly because vortices for 2D systems have longer lifetimes than those for 3D systems due tothe specific property of 2D systems called ’inverse energy cascade’, and such long-life vortices destabilize jet
oscillations.
In this simulation, mode transitions between the first and second modes were not observed, although they
were observed in the range 12 ≤ U ≤ 17.5 m/s in Brown’s experiment. A dynamical transition from the second
to the first was merely observed at U = 20m/s. We suspect reasons that the numerical setup may lack accuracy,
namely the grid size is not small enough.
The radiation intensity of sound waves took the maximum values in the vertical direction, while the soundintensity became smaller along the horizontal line due to the interference between the upper and lower soundfields in opposite phases. This is a characteristic of the dipole radiation. Actually, a pair of pressure spots with
opposite phases were observed above and below the edge, and apparently worked like a dipole-like pressuresource, namely, anti-symmetric sound waves seemed to be radiated from them. However, the comparison among
the compressible LES, incompressible LES and FDTD indicates the following facts. The pressure spots mostly
form the fluid pressure of the solenoidal velocity field and a tiny part of them is attributed to acoustic feedback.
Thus, the feedback mostly comes from the fluid velocity and/or fluid pressure, and the acoustic feedback makes
a smaller but non-negligible contribution.

ACKNOWLEDGEMENTS
The present work was supported by Grant-in-Aid for Scientific Research (C) Nos. 19K03655 from the Japan
Society for the Promotion of Science (JSPS) and “Joint Usage/Research Center for Interdisciplinary Large-Scale
Information Infrastructures” and “High Performance Computing Infrastructure” in Japan (Project ID: jh220001).

REFERENCES[1] Lighthill MJ. On sound generated aerodynamically. Part I: General theory. Proc. Roy. Soc. London A. 1952;
211: 564-587.
[2] Howe MS. Acoustics of Fluid-Structure Interactions. Cambridge, UK: Cambridge Univ. Press; 1998.
[3] Brown GB. The vortex motion causing edge tones. Proc Phys Soc. 1937; 49: 493-507.
[4] Powell A. On the edgetone. J Acoust Soc Am. 1961; 33: 395-409.
[5] Holger DK, Wilson TA, Beavers GS. Fluid mechanics of the edgetone. J. Acoust. Soc. Am. 1977; 62:1116-1128.
[6] Kaykayoglu R, Rockwell D. Unstable jet-edge interaction. Part 1. Instantaneous pressure fields at a single
frequency. J Fluid Mech. 1986; 169: 125–149.
[7] Kaykayoglu R, Rockwell D. Unstable jet edge interaction Part 2: Multiple frequency pressure fields. J Fluid
Mech. 1986; 169: 151-172.
[8] Crighton DG. The jet edge-tone feedback cycle; linear theory for the operating stages. 1992 J Fluid Mech.
1992; 234: 361–391.
[9] Nagy PT, Szabó A, Paál G. A feedback model of the edge tone, using the adjoint Orr–Sommerfeld equation.
J Fluid Mech. 2021; 915: A13.

[10] Fletcher NH, Rossing TD. The Physics of Musical Instruments, 2nd ed. New York, USA: Springer-Verlag;
1998.
[11] Hirschberg A. Aero-acoustics of wind instruments in Mechanics of Musical Instruments. Eds. A.Hirschberg,
J.Kergomard and G.Weinreich. Vienna, Austria and New York, USA: Springer-Verlag; 1995: 291-369.
[12] Miyamoto M, et al. Numerical study on acoustic oscillations of 2D and 3D flue organ pipe like instrumentswith compressible LES. Acta Acustica United Acustica. 2013; 99: 154–171.
[13] Tabata R, et al. Three-dimensional numerical analysis of acoustic energy absorption and generation in an
air-jet instrument based on Howe’s energy corollary. J Acoust Soc Am. 2021; 149: 4000-4012.
[14] Paál G, Vaik I. Unsteady phenomena in the edge tone. Int J Heat and Fluid Flow. 2007; 28: 575–586.
[15] Dougherty NS, Liu BL, O’Farrell JM. Numerical Simulation of the Edge Tone Phenomenon. NASA Contractor Report. 1969; 4581.
[16] Iwagami S, et al. Reproducibility of mode transition of edge tone with DNS and LES. Proc ICA 19; 9-13
September; Aachen, Germany 2019. p. 5573-5589.
[17] Iwagami S, Ryoya T, Kobayashi T, Hattori Y, Takahashi K. Numerical Study on Edge Tone with Compressible Direct Numerical Simulation: Sound Intensity and Jet Motion. Int J Aeroacoust. 2021; 34: 283-316.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022, in Gyeongju, Korea
Extended abstractABS-0301

Characterization of vehicle interior noise due to external flow
disturbance according to resonant transmission path throughwindows
Songjune LEE1; Cheolung CHEONG2;
1

Pusan National University, Korea

2

Pusan National University, Korea

ABSTRACTThe vehicle interior noise caused by high-speed external flow is one of the critical issues for productdevelopers to consider in a design state. The external flow disturbances consist of incompressible andcompressible waves. The former is associated with the turbulence fluctuation and the latter is related to theacoustic waves. Although the magnitudes of the compressible components were generally lower than thoseof the compressible ones, its contribution to the interior noise level cannot be neglected because thetransmission paths of incompressible and compressible pressure waves through the wind shield and window
glass of the vehicle are quite different from each other. In this study, the contribution of incompressible andcompressible pressure fluctuations to internal noise according to the resonant transmission path wereanalyzed. First, Large Eddy Simulation (LES) techniques were employed to accurately predict the external
flow field including the acoustic field around a vehicle. Second, surface pressure fluctuations on the vehicle
front wind shield and side windows were decomposed into incompressible and compressible ones using thewavenumber-frequency analysis. Lastly, the interior sound pressure levels are predicted according to theresonant transmission path by using Statistical Energy Analysis (SEA).
Keywords: Flow Noise, Vehicle Interior Noise, Statistical Energy Anaysis

1. INTRODUCTION
The vehicle interior noise caused by high-speed external flow is one of the critical issues for
product developers to consider in a design state. The improvement of the NVH (Noise, Vibration andHarshness) technologies has led to a significant reduction in vehicle noise caused by vibration froman engine, the interaction of tire/road, and transmission system (1). The sound power of aerodynamic
noise is known to increase with V6 and V8 for dipole and quadrupole sources, where V is the cruising
speed of the vehicle. On the other hand, the structure-borne noise from an engine, tire-road interaction
and a trans-mission system are only proportional to between V and V3 (2). This implies that the aerodynamic noise should be more dominant as the running speed of the vehicle increases. Aerodynamic
noise becomes even more critical due to the rapid commercialization of electric vehicles without
traditional combustion engine noise. The physical process of the interior transmission of external flow
disturbances shall be understood by three sequential mechanisms: external flow excitation on window
shields of a vehicle, the vibrational response of the vehicle windshields to the external flow
disturbances, and the acoustic response of a cabin room to the windshield vibration.
In this study, a reliable, systematic numerical methodology is proposed for the accurate andefficient prediction of the interior noise of a high-speed vehicle due to external flow disturbances. The
developed numerical methods consist of three sequential methods, which are suitable to each physicalsteps during the indoor transmission of external compressible and incompressible surface pressure
fields. In the first step, the large eddy simulation (LES) technique with high -resolution grids is used
for the accurate computation of both external aerodynamic and its corresp onding aeroacoustic fields
around a vehicle. In the second step, the wavenumber-frequency transform is used to decompose the12sjlee@pusan.ac.kr
ccheong@pusan.ac.kr

surface pressure fluctuations on the windows of a vehicle into the incompressible and compressible
ones. The separation is based on the physical fact that the phase speeds of incompressible andcompressible pressure waves are different from each other. Finally, the injected power formula thatreflects the vibration characteristics of the structure was defined, and a method that can be applied topractical problems was presented. The interior sound pressure levels are predicted by solving the one way vibro-acoustic FE model and SEA with input of each incompressible and compressible pressure
fluctuations. The developed numerical methods are applied for the benchmark problem of the HSM.

2. NUMERICAL SETUP
2.1 Numerical Setup of LES for External Flow
The entire computational domain and the target vehicle model is shown in Figure 1 and 2. The
dimensions of the entire computation domain are set to be large enough to allow any flow and acoustic
disturbances generated around a car body to leave without any reflection from the boundary plane,
which is critical for accurate aeroacoustic simulation. The whole computational domain consists ofabout 250-million cells which are constructed using the Fluent Meshing (version: 19.1) .

Figure 1 – Target model of Hyundai Simplified Model (HSM)

Figure 2 – Entire computational domain: dimensions of computational domain with boundary conditions
applied, where H denote height of HSM.

2.2 Numerical Setup of SEA for Interior Noise Calculation
SEA is based on the power balance equations in which the input power to subsystems is either
dissipated within the subsystems or transmitted to coupled subsystems. In order to apply SEA, it isnecessary to divide the system into appropriate subsystems and evaluate model parameters that
determine the dissipated and transmitted power in each subsystem. Once this is done the response
variables can be evaluated.

Figure 3 – Power flow in four subsystems of SEA model
Figure 3 shows the SEA subsystem. According to its physical component, the subsystem can bedivided into four subsystems, i.e., one acoustic cavity, one front windshield glass, and two side
windows glass. The power balance equations can be assembled in the following matrix.
𝐸1,𝑡𝑜𝑡
𝜂11
−𝜂41
Π1,𝑖𝑛
0
0
−𝜂
𝐸
0
𝜂
+
𝜂
0
Π
42
2,𝑡𝑜𝑡
24
{ 2,𝑖𝑛 } = 𝜔 [ 0 22]
−𝜂43
𝜂33 + 𝜂34
𝐸3,𝑡𝑜𝑡0
Π3,𝑖𝑛−𝜂14 −𝜂24−𝜂34 𝜂44 + 𝜂41 + 𝜂42 + 𝜂43 {𝐸4,𝑡𝑜𝑡 }0(1)

The injected power by the surface pressure fluctuations to the window glass can be written in the form,

𝑃(𝜔) =𝑀2
𝜋𝐴∑ |𝑃𝑀 (𝜔)|2
4𝑚𝑠
𝑀1

(2)

3. CONCLUSIONS
Finally, the numerical result obtained by applying the flow -vibroacoustic methods to the HSM iscompared with the measured data. Figure 6.1 compares the calculated interior noise spectra with themeasured one for the HSM using the injected power formula. Figure 4 compares the calculated interior
noise spectra with the measured one for the HSM using the injected power formula of Equation. It c an
be found that the numerical result obtained by combining the total surface pressure field from thehigh-resolution LES simulation result with the FE-SEA methods shows excellent agreement with themeasured data. It is seen that the interior wind noise is dominated by the acoustic surface pressure
field as the frequency increases, although the exterior acoustic energy is less than that of thehydrodynamic one in the corresponding frequency bands. This result reveals that the transmission
efficiency of acoustic excitation is much higher than that of hydrodynamic excitation. Especially, thesharp increase in the relative contribution of compressible acoustic pressure is observed to begin in
the frequency band around 4 kHz.

Figure 4 – Comparison of numerical and measured interior noise levels

ACKNOWLEDGEMENTS
This work was supported by the National Research Foundation of Korea(NRF) grant funded by the
Korea government(MSIT) (No. 2020R1F1A1066701).

REFERENCES
1. Peric C, Watkins C. Lindqvist, E. Wind turbulence effects on aerodynamic noise with relevance to roadvehicle interior noise. J. Wind Eng. Ind. Aerodyn. 1997;69, 423-435.
2. Ono K, Himeno,R, Fukushima T. Prediction of wind noise radiated from passenger cars and its evaluation
based on auralization. J. Wind Eng. Ind. Aerodyn. 1999;81, 403-419.
3. Davies H. G. Sound from turbulent-boundary-layer-excited panels, J. Acoust. Soc, 1971;49, 878-889.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022, in Gyeongju, Korea
Extended abstractABS-0549

Aeroacoustic-structural interactions of a multi-panel airfoil
configuration for tonal noise reduction
Irsalan ARIF1; Muhammad Rehan NASEER2; Garret Chi Yan LAM3; Randolph Chi Kin LEUNG4
Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hong Kong

ABSTRACTIn this paper, a multi-panel airfoil configuration (MPC) is designed to achieve airfoil tonal noise reduction
over a wide range of angle of attack (AoA) at a Reynolds number of 50000 and a Mach number of 0.4. The
aeroacoustic-structural interactions of the designed airfoil are explored using reduced order modelling(ROM). The range of operational AoA for the present study is chosen from 1° to 7° to analyze the tonalcomponent of airfoil noise. The design methodology of the multi-panel airfoil is based on the preliminary
analysis of the rigid airfoil to ascertain the optimum panel locations and their structural properties.
Subsequently, an airfoil configuration based on three resonant elastic panels with different structuralproperties is designed and its noise reduction potential is assessed at varying AoAs. ROM analysis shows anon-linear response in the noise reduction characteristics for the airfoil ranging from 6.75 dB to 7.92 dB overthe complete range of AoA. The structural analysis shows a complex vibration pattern for all the panels whichclearly indicates the presence of complex structural interaction among the panels for MPC airfoil at varying
AoA.
Keywords: Aeroacoustics, Tonal noise, Vibrations

1.

INTRODUCTION

Self-noise generation of an airfoil operating at low/moderate freestream Reynolds number ( Re) is
one of the most undesirable aspects associated with its operations [1-3]. Over the years, researchers
have studied and explored the phenomenon of airfoil self-noise generation which involves theinteraction among different physical mechanisms involving hydrodynamics, acoustics, and evenstructural dynamics in some cases [4-7]. Motivated by the flexibility of the bat wings and its
adaptability features, flexible wings/airfoils have received significant attention in past few decades
due to their favorable characteristics at low Re flow and improved airfoil aerodynamics at certain flow
conditions [8-10]. The membrane wings/airfoils are found to have better static stability [11] as wellas high lift to drag ratio as compared to rigid wing/airfoil [12]. Furthermore, these flexible airfoils
have shown to be effective in delaying stall characteristics at high AoA [9]. However, the existing
methods are limited to provide tonal noise reduction at a specific design condition only and may notremain effective for an airfoil operating at variable loading condition such as variable angle of attack(AoA). In this study, a multi-panel airfoil configuration (MPC) is designed with an aim to achieve
tonal noise reduction at a wide range of operating AoA.

1

irsalan.arif@connect.polyu.hk
rehan.naseer@connect.polyu.hk
3garret.lam.hk@connect.polyu.hk
4
randolph.leung@polyu.edu.hk
2

2.

METHODOLOGY

The present study utilizes high-fidelity direct aeroacoustic simulation (DAS) for its capability toresolve the coupling between the unsteady airfoil aerodynamic and acoustic solutions with highaccuracy [13]. To solve the unsteady compressible Navier-Stokes (N-S) equations, conservation
element and solution element (CE/SE) method is adopted. Since, it is t oo prohibitive in extensive
deployment of resources and time to search for optimal design with DAS, a Reduced Order Model(ROM) is developed and successfully implemented. ROM only requires 10% of the computationaltime required for its corresponding DAS simulation and can provide a reasonable qualitative
assessment of tonal noise reduction by the designed configuration [14].
The adopted methodology for the design of multi-panel configuration for different AoAs ranging from 1°
to 7° is divided into three major stages as shown in Figure 1. In Stage 1, the flow characteristics of the rigid
airfoil (RS) at selected AoAs are determined individually by DAS. The results of DAS analyses also help in
determining the steady base flow at respective AoAs for subsequent ROM analyses. In the next stage (Stage2), the airfoil configuration with single elastic panel is designed for each AoA. The structural properties andsuitable location of the panel on the airfoil surface at each AoA are determined based on the rigid airfoil
characteristics evaluated in Stage 1. In the final stage (Stage 3), a conceptual design of a multi-panel
configuration is presented which is aimed to possibly achieve tonal noise reduction at different AoAs. The
structural properties and locations of the elastic panels in this configuration are based on the ROM results
obtained in Stage 2. Finally, the effectiveness of the designed multi-panel configuration in airfoil tonal noise
reduction is evaluated at different AoAs by PEM. The final schematic sketch of the multi-panel airfoil
configuration (MPC) designed for the present study is shown in Figure 2.

Figure 1 – Designed methodology

Figure 2 – Schematic sketch of the MPC design concept

3.

RESULTS AND DISCUSSION

The effectiveness of MPC in tonal noise reduction at different AoAs is evaluated with ROM analysis. Figure3(a)-(c) show the azimuth plots of p’rms at r = 3 for both RS and MPC at each AoA. At AoA = 5° (Figure 3(b)),
a significant reduction in p’rms is observed at all azimuth locations for MPC as compared to RS. Furthermore,
the azimuth plot for MPC appears to be asymmetric around θ = 0° where the reduction in p’rms appears to besignificant in the third quadrant. At AoA = 3° (Figure 3(a)), a reduction in p’rms is observed for most azimuth
locations; however, a slight amplification is also observed between 120° ≤ θ ≤ 140°. At AoA = 7°, thereduction in p’rms in first quadrant is much higher than AoA = 3° and a greater region of amplification in p’rms
is also observed between 120° ≤ θ ≤ 170°.
The extent of noise reduction achieved by MPC is evaluated by analyzing the ∆SPL = SPLRS – SPLMPC atdifferent AoAs and shown in Figure 3(d). The noise reduction achieved by MPC at AoA = 5° is much higher
than other AoAs where an average reduction of 4.41 dB is observed with a maximum reduction of 7.92 dB at
θ = 185°. At AoA = 3°, an overall average noise reduction of 2.20 dB is observed with a maximum reductionof 7.73 dB at θ = 178°. However, a maximum noise amplification of 1.46 dB is also observed at θ = 126°. At
AoA = 7°, an overall average noise reduction of 1.41 dB is observed with a maximum reduction of 6.75 dB
at θ = 60° but a maximum noise amplification of 1.70 dB is also observed at θ = 164°. Table 1 shows acomparative analysis of noise reduction at all AoAs along with the noise reduction achieved by thecorresponding single-panel configurations. It is interesting to observe that an enhancement in the maximum
noise reduction is achieved by MPC as compared to single-panel configuration at each AoA; however, theaverage noise reduction is reduced for AoA = 3° and remains almost similar at AoA = 7°. The overall noise
reduction for MPC is observed to be highest at AoA = 5° whereas the highest noise reduction for single-panel
configuration is observed at AoA = 3°. The possible cause of higher noise reduction at AoA = 5° for MPC
may be attributed to the fact that all the panels are exposed to region of high boundary layer flow instabilities
at this AoA as compared to that for AoA = 3° and 7°. Furthermore, the panels’ inter-dynamical interactions
appear to play a critical role in enhancing/degrading the noise reduction of panel-airfoil configuration.
However, exploration of these effects would require multiple DAS calculations for better in-depth evaluation
which is left to future study.

Figure 3 – Comparison of azimuth distributions of p’rms at r = 3 between MPC and RS. (a) AoA = 3°, (b)AoA = 5°, (c) AoA = 7°. ——, RS; ——, MPC; and (d) Comparison of azimuthal distribution of ∆SPL at
r = 3 between MPC and respective RS. ——, AoA = 3°; ——, AoA = 5°; ——, AoA = 7°. The area shadedin red indicates SPL amplification.
Table 1 – Effectiveness of multi-panel configuration at different flow conditions

4.

CONCLUSIONSA multi-panel configuration (MPC) based on three elastic panels is designed to provide tonal noise reduction
over a range of AoA. ROM analysis shows a non-linear response in the noise reduction characteristics for theairfoil ranging from 6.75 dB to 7.92 dB over the complete range of AoA. The study can further help in thedesign of a noise control method which is effective for a range of airfoil operating conditions.

ACKNOWLEDGEMENTS
The authors gratefully acknowledge the support from the Research Grants Council of theGovernment of Hong Kong Special Administrative Region under grant number 15208520. The firstand fourth authors are grateful to a generous research donation from Philip K. H. Wong Foundation
under grant number 5-ZH1X (now N-ZH1X). The third author is grateful to stipend support to his
study from the Department of Mechanical Engineering, The Hong Kong Polytechnic University.

REFERENCES
1. Arbey, H. and Bataille, J., Noise generated by airfoil profiles placed in a uniform laminar flow. Journalof Fluid Mechanics. 1983(134):33–47.
2. Brooks, T. F., Pope, D. S., and Marcolini, M. A., Airfoil self-noise and prediction. In: NASA Reference
Publication. 1989.
3. Fink, M. R., Prediction of airfoil tone frequencies. Journal of Aircraft. 1975(12):118–120.
4. Arcondoulis, E., Doolan, C. J., Zander, A. C., Brooks, L. A., and Liu, Y., An investigation of airfoil dual
acoustic feedback mechanisms at low to-moderate Reynolds number. Journal of Sound and Vibration.
2019(460):114887.
5. Desquesnes, G., Terracol, M., and Sagaut, P., Numerical investigation of the tone noise mechanism overlaminar airfoils. Journal of Fluid Mechanics. 2007(591):155–182.
6. Jones, L. E. and Sandberg, R. D., Numerical analysis of tonal airfoil self-noise and acoustic feedbackloops. Journal of Sound and Vibration. 2011(330):6137–6152.
7. Arif, I., Lam, G. C. Y., Wu, D., and Leung, R. C. K., Passive Airfoil Tonal Noise Reduction by Localized
Flow-Induced Vibration of an Elastic Panel. Aerospace Science and Technology. 2020(106319).
8. Smith, R. and Shyy, W., Computation of unsteady laminar flow over a flexible two-dimensional
membrane wing. Physics of Fluids. 1995(7):2175–2184.
9. Lian, Y. and Shyy, W., Laminar-turbulent transition of a low Reynolds number rigid or flexible airfoil.
AIAA Journal. 2007(45):1501–1513.
10. Gordnier, R. E., High fidelity computational simulation of a membrane wing airfoil. Journal of Fluids andStructures. 2009(25):897–917.
11. Stanford, B., Sytsma, M., Albertani, R., Viieru, D., Shyy, W., and Ifju, P., Static aeroelastic model
validation of membrane micro air vehicle wings. AIAA Journal. 2007(45):2828–2837.
12. Stanford, B., Ifju, P., Albertani, R., and Shyy, W., Fixed membrane wings for micro air vehicles:
Experimental characterization, numerical modeling, and tailoring. Progress in Aerospace Sciences.
2008(44):258–294.
13. Lam, G. C. Y., Leung, R. C. K., Seid, K. H., and Tang, S. K., Validation of CE/SE scheme in low Mach
number direct aeroacoustic simulation. International Journal of Nonlinear Sciences and Numerical
Simulation. 2014(15):157–169.
14. Arif, D. Wu, G. C. Y. Lam, and R. C. K. Leung, “Exploring airfoil tonal noise reduction with elastic panel
using perturbation evolution method. AIAA Journal. 2020(58): 4958–4968.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022, in Gyeongju, Korea
Extended abstractABS-0899

Control of flow-induced noise by structural compliance
Muhammad Rehan NASEER1; Irsalan ARIF2; Randolph Chi Kin LEUNG3
Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hong Kong

ABSTRACT
Flow-induced noise generation by external flow devices operating at low to intermediate Reynolds number
is an overriding concern associated with their design and operations. Over the years, a number of passive
noise control methods have been proposed and developed, however their implementation is limited by the
associated aerodynamic performance degradation. In this regard, we propose a novel method of utilizing thestructural compliance for noise reduction of external flow devices with minimum or no sacrifice in the overall
aerodynamic characteristics. The key idea is to design a structurally compliant elastic surface that vibrates instructural resonance fluid loading for absorbing the energy from the flow to sustain its vibration. We have
implemented the method for the two unique noise generation problems: a deep cavity flow driven by flowacoustic resonance and a symmetric airfoil exhibiting feedback phenomenon. The effectiveness of thecompliant surface in tonal noise reduction for both test cases is analyzed numerically using high-fidelity
direct aeroacoustic simulations. Despite the prevalence of different flow regimes, the application of compliant
surface provides a significant overall noise reduction for each case up to different extents. Design strategy of
the compliant surface along with its limitations are also discussed
Keywords: Airfoil Tonal noise, Deep Cavity, Structural Compliance

1.

INTRODUCTION

Flow-induced noise generation by external flow devices operating at low to intermediate Reynolds
number is an overriding concern associated with their design and operations. Some of the mostcommon physical problems involving flow-induced noise are flow passing over a deep cavity andover the airfoil. Flow-induced noise generation by external flow devices operating at low tointermediate Reynolds number is an overriding concern associated with their design and operations.
Two of the most common physical problems involving flow-induced noise are flow passing over a
deep cavity and over the airfoil. Flow over a deep cavity produces intense noise [1-3], if potent enough,it may damage the nearby structure upon exposure. Similarly, self-sustained noise generation by anairfoil [4-6] operating at low/moderate freestream Reynolds number is also a significant challenge
which merits scientific investigation for the feasible suppression measure. The underlying mechanism
governing both the problems is the feedback loop [6-8] between the streamwise moving shear layer
and the incident acoustic waves. However, the intimate manner of the aeroacoustic interaction in caseof cavity flow slightly differs from the airfoil feedback phenomenon. The favorable phase relationshipbetween the upstream travelling convective disturbances and the incoming acoustic fluctuation at the
point of shear layer excitation has been regarded by several authors [4, 6, 9, 10] the main contributor
towards the establishment of the aeroacoustic resonance. Therefore, by invoking a phase delay to
disrupt the feedback process could be one of the measures for the noise abatement. In recent times,
the idea of flow compliant surface has gained attention due to its flexibility in application and theadaptability in compliance to the incident flow, which makes it a suitable candidate for our noise
reduction strategy [4, 11, 12]. The aim of the current study is therefore to leverage the potential of an1rehan.naseer@connect.polyu.hk
irsalan.arif@connect.polyu.hk
3
randolph.leung@polyu.edu.hk
2elastic panel based on its flow compliant characteristics to suppress the tonal noise generation in the
airfoil and cavity flow problems.

2.

METHODOLOGY
The present study utilizes high-fidelity direct aeroacoustic simulation (DAS) for its capability toresolve the coupling between the unsteady airfoil aerodynamic and acoustic solutions with high accuracy. To
solve the unsteady compressible Navier-Stokes (N-S) equations, conservation element and solution element(CE/SE) method [13] is adopted and to model the nonlinear response of the elastic, one dimensional plate
equation has been implemented [14].
The novel concept of incorporating the flow complaint surface to reduce the tonal noise emission has
been successfully implemented for the two external flow cases. First, we tested a deep cavity flow operating
at low Mach number of M = 0.09. In this flow regime the deep cavity generates a strongly resonatedaerodynamic noise. Such an exacerbated response of the deep cavity flow occurs due to the in-phaserelationship between the longitudinally oscillating acoustic mode and the streamwise moving convective
disturbances of the shear layer oscillation. The sites around the cavity which promote the onsetting of thenexus between the later and the former are the walls adjacent to the leading and trailing edges of the cavity
along with the bottom surface which is exposed to the maximum acoustic pressure. In order to disturb thestrongly resonant aeroacoustic feedback process responsible for the higher noise radiation, it is therefore
imperative to install the elastic panel at the aforementioned locations. It is anticipated that throughaeroacoustic structural interaction (or acoustic-structural interaction based on the elastic panel mounting
location and its exposure to the prevalent flow regime), we could be able to achieve the noise reduction bychannelizing the flow energy into the sustained panel vibration. In essence, the mutual strengthening of theshear layer and cavity acoustic mode has been targeted for the ultimate noise suppression using the elastic
panel vibration.
For the second case, flow over a symmetric airfoil operating at low Reynolds number of 50,000 and
Mach number of M = 0.4 which produces a sharp tonal noise involving aeroacoustic feedback loop. We aim
to leverage the flow energy absorption phenomenon with self-sustaining panel for effective suppression of
airfoil boundary layer flow unsteadiness before their eventual scattering as noise. The optimum location,
length and structural properties of the panel are carefully chosen based on the flow characteristics of the rigid
airfoil. For the present study, a short elastic panel of 5% of airfoil chord is chosen which is located at 40%
airfoil chord due to presence of onset of sharp rise in boundary layer flow instabilities at this location asshown in Figure 2(a). The structural properties of the panel are set in a manner that the panel vibrates inresonance with the flow induced loadings.

3.

RESULTS AND DISCUSSION
Case 1: Fig 1. explains the application of flow complaint surface in reducing the sound pressurelevel (SPL) of open cavity flow. In case of rigid cavity, the shear layer and standing mode remains in-sync
with each other which promotes the resonance where the acoustic mode has the dominant role to play bymaking the shear layer to grow in a certain way along the cavity opening. Upon the enactment of the noise
control strategy, the bottom wall of the cavity is replaced with an elastic panel. With the envisaged acousticstructural interaction the acoustic component gets affected as the amplitude of the standing acoustic waves
along the cavity depth is reduced to the 40% of its rigid cavity (RC). The reduction of acoustic component
effectively retarded the previously maintained feedback loop with the shear layer growth became independentof the former. Hence the installation of elastic panel reduced the SPL by 3.6 db.

Figure 1. Implementation of noise suppression method of using flow compliant surface at the bottom of thecavity. The encapsulated dashed region infers the cavity acoustic mode and shear layer interaction being
affected with elastic panel application leading to the lower sound pressure level.

Case 2:The effect of airfoil configuration with elastic panel (EP) on the acoustic radiation isanalyzed and compared with rigid airfoil (RS) by plotting the azimuth variations of p’rms at a radial locationof r = 3 above the airfoil trailing edge and shown in Figure 2(b). The reduction in p’rms is observed to besignificant in all directions with much higher reduction toward the forward plane. The acoustic characteristics
of RS and EP airfoils are evaluated and compared by analyzing their SPL spectra above the airfoil trailingedge and shown in Figure 2(c). The spectra of both RS and EP airfoils remain similar where a maximum
noise reduction of 7 dB is observed for the EP airfoil at the peak frequency of f = 3.37.

PanelFigure 2. (a) Schematics of the designed airfoil configuration; (b) p’rms comparison of RC and EP
configurations at a radial location of r = 3; and (c) SPL spectrum of RC and EP configurations at a radial
location of r = 3.

RC,

EP.

Figure 3 illustrates the filtered FFT data of v’ and p’ flow field data at f = 3.37 for RS and EP airfoils.
For EP airfoil, no shift in the dominant frequency is observed. The vortex shedding pattern is observed to be
similar for both the cases; however, the strength of v’ and p’ is significantly reduced for EP airfoil. A
maximum noise reduction is achieved at this frequency by EP airfoil as observed in Figure 2(c).

RS

EP

RS

EP

Figure 3. Filtered FFT distribution of v’ [i.e., (a) and (b)] and p’ [i.e., (c) and (d)] at f = 3.37 for RS and EP
airfoils.

4.

CONCLUSIONSThe effect of structural compliance for flow-induced noise control is successfully implemented anddemonstrated for two unique external flow cases. For the case of flow over the deep cavity, an elastic panel
is implemented at the bottom wall and a noise reduction of 3.6 dB is achieved. For the case of flow over anairfoil, the panel is mounted at 40% chord location and a noise reduction of 7 dB is achieved. The method
can be implemented in other flow-induced noise problems with careful panel design considerations.

ACKNOWLEDGEMENTS
The authors gratefully acknowledge the support from the Research Grants Council of theGovernment of Hong Kong Special Administrative Region under grant number 15208520. The firstauthor is grateful to stipend support to his study from the Department of Mechanical Engineering, The
Hong Kong Polytechnic University. The second and third authors are grateful to a generous research
donation from Philip K. H. Wong Foundation under grant number 5-ZH1X (now N-ZH1X).

REFERENCES
1. L. East, "Aerodynamically induced resonance in rectangular cavities," Journal of sound vibration, vol. 3,
no. 3, pp. 277-287, 1966, doi: 10.1016/0022-460X(66)90096-4.
2. Y. W. Ho and J. W. Kim, "A wall-resolved large-eddy simulation of deep cavity flow in acoustic
resonance," Journal of Fluid Mechanics, vol. 917, 2021.
3. H. Yokoyama, K. Otsuka, K. Otake, M. Nishikawara, and H. Yanada, "Control of cavity flow withacoustic radiation by an intermittently driven plasma actuator," Physics of Fluids, vol. 32, no. 10, p.
106104, 2020.
4. I. Arif, G. C. Y. Lam, R. C. K. Leung, and M. R. Naseer, "Distributed surface compliance for airfoil tonalnoise reduction at various loading conditions," Physics of Fluids, vol. 34, no. 4, p. 046113, 2022.
5. I. Arif, G. C. Y. Lam, D. Wu, and R. C. K. Leung, "Passive airfoil tonal noise reduction by localized flowinduced vibration of an elastic panel," Aerospace Science Technology, vol. 107, p. 106319, 2020.
6. G. C. Y. Lam and R. C. K. Leung, "Aeroacoustics of NACA 0018 Airfoil with a Cavity," AIAA Journal,
vol. 56, no. 12, pp. 4775-4786, 2018.
7. D. Rockwell and E. Naudascher, "Review—Self-Sustaining Oscillations of Flow Past Cavities," Journalof Fluids Engineering, vol. 100, no. 2, pp. 152-165, 1978, doi: 10.1115/1.3448624.
8. J. E. Rossiter, Wind-tunnel Experiments on the Flow Over Rectangular Cavities at Subsonic andTransonic Speeds. H.M. Stationery Office, 1967.
9. G. A. Bres and T. Colonius, "Three-dimensional instabilities in compressible flow over open cavities,"
Journal of Fluid Mechanicsvol. 599, pp. 309-339, 2008.
10. C. W. Rowley, T. Colonius, and A. J. Basu, "On self-sustained oscillations in two-dimensional
compressible flow over rectangular cavities," Journal of Fluid Mechanics, vol. 455, pp. 315-346, 2002.
11. H. K. H. Fan, R. C. K. Leung, G. C. Y. Lam, Y. Aurégan, and X. Dai, "Numerical coupling strategy for
resolving in-duct elastic panel aeroacoustic/structural interaction," AIAA Journal, vol. 56, no. 12, pp.
5033-5040, 2018.
12. G. C. Y. Lam, R. C. L. Leung, and S. K. Tang, "Aeroacoustics of duct junction flows merging at different
angles," Journal of Sound Vibration, vol. 333, no. 18, pp. 4187-4202, 2014.
13. G. C. Y. Lam, R. C. K. Leung, K. Seid, and S. K. Tang, "Validation of CE/SE scheme in low mach number
direct aeroacoustic simulation," International Journal of Nonlinear Sciences Numerical Simulation, vol.
15, no. 2, pp. 157-169, 2014.
14. H. K. H. Fan, R. C. K. Leung, and G. C. Y. Lam, "Numerical analysis of aeroacoustic-structural interactionof a flexible panel in uniform duct flow," The Journal of the Acoustical Society of America, vol. 137, no.
6, pp. 3115-3126, 2015.