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Prediction of the hydrodynamic noise of one certain frigate
Xiuhai LV1; Qian LIANG2; Dongyan SHI3; Qingshan WANG4 1 College of Mechanical and Electrical Engineering, Harbin Engineering University, PR China;
Heilongjiang Agricultural Engineering Vocational College, PR China 2 Harbin Engineering University, PR China 3 Harbin Engineering University, PR China 4 Harbin Engineering University, PR China
ABSTRACT
In this paper, the prediction for the hydrodynamic noise of one certain frigate at the speed of 16Kn is
made. The hydrodynamic noise is divided into the flow-induced noise and the noise from the
flow-induced vibration to study separately. Firstly, the numerical simulation for the flow-induced
noise is conducted by the Finite Element Method (FEM) and the Boundary Element Method (BEM),
and the flow noise distribution characteristics in steady state are analyzed from the horizontal and
vertical direction. Then, the noise from the flow-induced vibration is studied using the Statistical
Energy Analysis (SEA). Finally, the complete hydrodynamic noise of the frigate is acquired by the
stacking of the two results, which can be used to evaluate whether the design meets the requirements.
The study of this paper can provide the reference for the prediction of the hydrodynamic noise and
the further noise reduction to a degree.
Keywords: Hydrodynamic noise, Flow-induced noise, Noise from the flow-induced vibration,
FEM, BEM, Noise reduction I-INCE Classification of Subjects Number(s): 76.9
1. INTRODUCTION Recently, the acoustic stealth of the underwater vehicle has attracted more and more attention
of the researchers around the world and a great many efforts have been made. In these researches,
the studies of the hydrodynamic noise are scarce. But it does have the dominant effect on the
safety of ship voyage. So, it’s of great significance to conduct the numerical analysis of the
hydrodynamic noise of the ships and can provide the theoretical support for the design of
underwater vehicles.
The study of hydrodynamic noise can be classified two aspects: the flow induced noise and
noise of flow induced-vibration. For the flow induced noise, Liu et al. (1) simulated the flow field
around the fore using the Fluent and on this base, combined with the FW-H acoustic model,
calculated the sound pressure level of flow induced noise. Based on boundary layer theory and
radiated noise theory of boundary layer transition, Zhao et al. (2) presented an integrated
prediction method of torpedo flow noise. Heng et al. (3) adopted a hybrid method of combining
LES and FEM to predict the flow induced noise in a centrifugal pump. Zhang et al. (4) carried out
the numerical simulation of flow and flow-induced noise on a duct cavity by using Lighthill
acoustical analogy and LES method. The validation of the method was verified by comparing the
results with the experimental and computed results in some published literature. Jiang et al. (5)
studied the flow noise of underwater submarine based on the Boundary Element Method (BEM)
and the FW-H equation, and by comparison it’s seen that the results obtained by the BEM were
more close to the experiment results. For the noise of flow-excited noise, Durant et al. (6)
proposed a cross-like model of the wall pressure fluctuation to measure the vibroacoustic response
1 [email protected] 2 [email protected] 3 [email protected] 4 [email protected]
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of a thin cylindrical shell excited by a turbulent internal flow, and by the comparison with the
experiment results, an agreement within a few decibels is shown. Zhang et al. (7) performed
numerical studies for the predictions of cavity flow and flowed noise by LES and FW-H acoustic
analogy. Wei et al. (8) calculated the flow-excited noise via a refined integration algorithm of
sound field with the hull responses boundary condition. In addition, Wang et al. (9) made
separating prediction of the hydrodynamic noise of an underwater vehicle using the Large Eddy
Simulation (LES) and the Lighthill’s acoustic analogy method. In his paper, the hydrodynamic
noise was classified into four categories: the flow-induced noise of the shell, the noise of flow
excited-vibration of the shell, the flow induced-noise of the propeller, and the noise of flow
excited-vibration of the propeller.
So, in this paper, one certain frigate is taken as the study model, and by the separating
prediction strategy, its flow induced noise and noise of flow-induced vibration is simulated
respectively. The numerical simulation for the flow-induced noise is conducted by the Finite
Element Method (FEM) and the Boundary Element Method (BEM) and its distribution
characteristics in steady state are analyzed from the horizontal and vertical direction. The noise of
flow excited-vibration is studied using the Statistical Energy Analysis (SEA). On this basis, the
total hydrodynamic noise can be obtained therefore by the superposition of two types of noise.
The study of this paper can provide the reference for the prediction of the hydrodynamic noise and
the further noise reduction to a degree.
2. METHOD
The hydrodynamic noise is generated by the irregular and undulating sea water acting on the
ship. According to the different hydrodynamic effects, it can be classified into two types in general,
namely, the flow induced-noise and the noise of flow excited-vibration, where the former refers to
the direct radiation noise caused by the pulsating pressure and the latter is the radiation noise
generated by the vibration of the hull plate due to the pulsating pressure (9, 10). It can be
expressed as follows:
1 2p p pL L L (1)
Where, pL is the total hydrodynamic noise;
1pL and
2pL are the flow induced-noise and the
noise of flow excited-vibration respectively.
In this paper, the separating prediction for the two types of noise is conducted because of their
different forming mechanisms.
2.1 Theory and Method for Prediction of Flow Induced-noise
As one of the important parts of the hydrodynamic noise, the flow induced-noise is the direct
radiation noise caused by the pulsating pressure owing to the existence of the hull plate. The
calculation of it is on the basis of the Lighthill’s acoustic analogy theory to solve for the sound
filed. The Lighthill’s acoustic analogy theory is based on the Lighthill’s Equation which is derived
from the Viscous Fluid N-S Equation:
222
2 2
0
1 ''
ij
i j
TQF
c t t x x
(2)
The three terms on the right respectively represent the three dominant types of sources of
acoustic radiation (11):
Q
t
— Monopole, involving unsteady mass flow into the fluid, sound produced by movement
in fluid. The sound intensity is directly proportional to the cube of the velocity and the first power
of the Mach number. Monopoles are essentially omnidirectional, and examples are pulsating
bubbles, pistons in baffles and cavitation;
F — Dipole, the divergence of the unsteady forces applied at some boundary. Sound
produced by momentum fluctuations in fluid. The sound intensity is directly proportional to the
cube of velocity and the cube of Mach number. The dipole has cosine directional patterns and its
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radiation efficiency is lower than the monopole’s; 2
ij
i j
T
x x
— Quadrupole, involving turbulent stresses in the fluid itself, sound produced by the
fluctuation of momentum flow rate in fluid. The sound intensity is directly proportional to the
cube of the velocity.
At low Mach number, the lower the order of the source the more efficient it is as an acoustic
radiator. That is to say, when the monopole source exists, it does be the main acoustic source. But
for the fluid around the ships on the voyage, such acoustic source doesn’t exist in general, so the
dipole source caused by the pulsating pressure acting on the rigid body plays the dominant role.
When the ships are on the voyage, a considerable portion of the total power is converted into the
wake turbulence which is a typical type of the quadrupole sources. And since only when the
fluctuating velocity is close to the velocity of sound, the quadrupole source can be the main effect
factors, so when the ships sail at a low speed, the effect of the quadrupole source also can be
ignored.
In this paper, a hybrid method of combining FEM and BEM is used to make a prediction for
the flow induced-noise. The Finite Element Method for fluid flow is adopted to solve for the
dipole component in the Lighthill’s equation; using it as the boundary condition and solving for
the Helmholtz equation with the Green’s function, the sound pressure level of each point in the
fluid field can be obtained.
Specifically, the FEM model of the boundary of the frigate is built according to its hull lines
firstly; then the dipole sources of the points along the boundary are calculated using the software
ANSYS-CFX; lastly, using the above obtained results as the input boundary condition and
utilizing the acoustic boundary element module in LMS Virtual Lab, sound pressure levels of the
points in the fluid field are calculated.
Before calculating the Lighthill stress, the fluid field boundary of the ships should be modeled.
Because of the symmetry, the model is simplified and only half model of the ship is built to
decrease the calculation cost, which is shown in Fig. 1.
(a) Geometry model of the underwater part of ship
(b) ICEM-CFD model
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(c) Analysis model and CFX calculation model
Figure 1 – Model for prediction of flow induced-noise
2.2 Theory and Method for Prediction of Noise of Flow Excited-vibration
Turbulent fluctuating pressure is the load with characteristics of wide frequency band, high
frequency and random surface distribution. Under the effect of turbulent fluctuation pressure, at
the high-frequency band, the vibration modal of the structure and the motivated vibration modal or
acoustic modal in the sound field are very dense, the random superposition of which makes the
distribution of the vibration response of the structure and the spatial sound field trend to be
well-distributed and there are no obvious spatial peak and valley points any longer. So for the
description of the system characteristics, it makes full use of the fact that there are many vibration
modals in the certain frequency band, and the statistic is adopted to express the dynamic
characteristics of the system, where the “energy” is treated as the independent dynamic variables.
Therefore, the Statistical Energy Analysis (SEA) is adopted to make prediction of the structural
acoustic radiation excited by the turbulent fluctuating pressure.
According to the fundamental principle of SEA, to solve for the energy-balance equation, the
power input to the subsystem should be known first. At the present stage, except for the
experiment, the empirical formula method is also commonly used to determine the input power of
each subsystem. Firstly, the power spectrum density of the turbulent fluctuation pressure which is
input to the structure is estimated using the empirical formulas, and then the input power iP can
be obtained by the by integration; lastly, the mean square pressure of the acoustic subsystem is
determined by solving the energy balance equation.
(1) Calculation for the wavenumber-frequency spectrum of turbulent fluctuation pressure
Referring to [12], Smol’yakov-Tkachenko model is adopted here.
( , ) 0.974 ( ) ( )[ ( , ) ( , )]p k A h F k F k (3)
Where, 2 1/2
* *( ) 0.124[1 ( ) ]
4 4
c cU UA
;
21 21
1 12
1( ) [1 ] 1 1.005
1.0256.515
m A Ah m G A m
AG
, ;
2 2 2 3/2( , ) [ (1 ) ( ) ]6.45
y cz ck Uk U
F k A
;
*
00.89 /2 2 2 2 3/2
1 1 0
1
1.005 ( , ) 0.995[1 {( ) ( ) }] 0.59 0.30
y c Uz c
c
k Uk UF k A m m U U e
m
1/5
* 4/5
0
0.0360 xU
is the displacement thickness of laminar boundary layer; is the
kinematic viscosity coefficient; zk and yk are the wavenumbers along two directions;
(2) structural input power caused by the fluctuating pressure
The generalized modal force of the surface of elastic structure acting by the turbulent
fluctuation pressure is expressed as follows:
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2
1 3 1 3 1 3, , ,mnp p mnk k k k dk dk (4)
Where, 1 3, ,p k k is wavenumber-frequency spectrum of turbulent fluctuation pressure,
1 3,mn k k is wave number function of vibration modal of elastic shell wall.
The interaction between turbulent fluctuation pressure and elastic shell can be classified into
the surface interaction and the angular interaction. For the interaction between turbulent
fluctuation pressure and underwater elastic shell, only the surface interaction needs considering.
So the integral in Eq. (4) can be approximated as:
2
1 34 , / , , /mnp pL ck U k A (5)
Where, pL is the low wavenumber component of the wavenumber-frequency spectrum of
turbulent fluctuation pressure; A is the area of the flat plate.
The power spectrum density input to the elastic shell by the turbulent fluctuation pressure in
the unit frequency band is expressed as Eq. (6):
124
mnp
L
nP
h
(6)
Where, 1L s
is the equivalent material density of cover wall considering the fluid
loading. s
is the material density of cover wall; 0
20
2 1
12 1
L
s f f
C
C M M
;
LC longitudinal
wave velocity of cover wall material; /f cM f f , 2
0 /cf C B m
is coincidence frequency.
(3) Once the wavenumber-frequency spectrum of turbulent fluctuation pressure is determined,
the input power in the frequency band corresponding to the frequency i can be obtained by the
following Eq.(7):
i
ii i iP P d
(7)
Where, 0 is the center frequency of one certain frequency band, is half frequency
bandwidth and it is taken as the1/3 frequency doubling.
3. Results
3.1 Prediction of Flow Induced-noise (16kn)
By extending the calculation time (total computing time t=7s) and controlling the calculating
time step (time step increment △t=5×10-5
s), the steady-state flow induced-noise distribution can
be obtained, seen in Fig. 2.
50Hz
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200Hz
400Hz
600Hz
1.2kHz
Vertical horizontal
Figure 2 – Flow induced-noise distribution in the typical frequency
From Fig. 2 the conclusion can be drawn that:
(1) In the horizontal direction, the flow induced-noise is mainly distributed in the bow and the
middle parts of the ship, and with the increase of the frequency, it transfers to the middle of the
ship gradually; in the vertical direction, the flow induced-noise is mainly distributed in the stern
and the middle parts of the ship, and as the frequency increases, it gradually transfers to the
middle of the ship, which is similar to that in the horizontal direction. Because of the
inconsistency between the calculation time and the convergence time, it can be thought that the
flow induced-noise is mainly distributed in the middle of the ship after steady convergence.
(2) By the comparison of the flow induced-noise in the horizontal direction and vertical
direction, is can be found that the distribution of the underwater sound field in the horizontal
direction is more uniform, which is very different from the vertical direction. On one hand, it may
owe to the fact that rational prolife design makes the distribution of the fluid field along the
direction of ship length more uniform and thereby generate the relatively low flow induced-noise.
On the other hand, the flow induced-noise of the stern spreads along the direction ship width,
which also causes the obviously lower noise level in the horizontal direction than the vertical
direction.
(3) For the flow induced-noise in the vertical direction, at low frequency, it is mainly
distributed at the stern and with the gradual increase of the frequency, it transfers to the middle
and front of the ship. The maximum flow induced noise is distributed in the vertical direction and
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the noise level in the horizontal direction is relatively low. Since the flow induced noise in the vertical direction plays the leading role, the detail results
with different computing time is presented in Table 1.
Table 1 – Sound band pressure level of flow induced noise (vertical) with different computing
times (dB)
Time, s
Frequency, Hz 0.15 1 7
20 147.3 121.3 93.6
25 146.3 120.3 96.7
31.5 148.1 125.2 93.5
40 144.5 128.5 95.8
50 142.5 129.1 97.8
63 144.7 128.8 99.2
80 141.8 120.4 103.4
100 141.1 115.1 104.8
125 134.9 118.2 97.7
160 141.6 120.5 107.5
200 136.3 116.9 110.7
250 136.1 110.1 110.7
315 140.9 123.7 112.3
400 132.3 128.5 113.5
500 136.9 127.1 117.6
630 131.2 120.0 119.2
800 131.7 124.5 121.5
1000 134.3 130.6 127.7
1250 124.3 123.5 116.7
1600 120.9 120.4 112.5
2000 132.4 117.7 110.2
2500 140.3 116.9 110.2
3150 147.6 115.4 103.6
4000 156.3 113.2 100.1
6300 161.2 110.7 96.3
8000 166.3 106.6 94.6
Total 168.1 137.9 130.1
It’s seen that with the increase of time, the flow induced noise gradually trends to be steady
and converges from 168.1dB to 130.1dB. The main reason for this phenomenon is that the false
turbulence of the model in the initial time leads to large turbulence in the bow which makes the
ship generate large flow induced-noise; but as the time goes on, the turbulence decreases gradually
and the boundary layer becomes stable, so the flow induced noise maintains at about 130.1dB. In
conclusion, at the present speed the flow induced noise of the ship is about 130dB.
3.2 Prediction of Noise of Flow Excited-vibration (16kn)
So according to the above analysis, to make prediction of noise of flow excited-vibration, the
SEA model of frigate should be built first and it is on the basis of type values, compartment
arrangement and a part of the typical structure layouts provided in the scheme design phase. The
complete SEA model is seen in Fig. 3(a). As for the input loads applied to the underwater hell, it’s
given in Fig. 3(b).
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(a) Calculation model
(b) Input power curve
Figure 3 – SEA model for prediction of noise of flow excited-vibration
The loss factor has close relationship with the noise of flow excited-vibration. However,
because of its uncertainty and varying with the different materials and structures, in this paper, two
extreme situations, namely, η=0.05% and η=0.1%, are taken to conduct the analysis and determine
the range of the noise of flow excited-vibration. The range of the loss factor is determined by two
factors: 1. the loss factor of the steel structure is η≈0.01%; 2. considering the effects of the
outfitting, welding, acoustic material and other factors in the actual ship, the upper limit is taken
as η=0.1%. Fig. 4 presents the distribution of the noise of flow excited-vibration at the speed of
16Kn.
(a) η=0.05%(f=1kHz)
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(b) η=0.1%(f=1kHz)
Figure 4 – Distribution of the noise of flow excited-vibration with two extreme situations
The detailed results for sound pressure spectrum level of the noise of flow excited-vibration
are listed in Table 2.
Table 2 – Sound pressure spectrum level of noise of flow excited-vibration with two extreme
situations (dB)
Frequency, Hz η=0.05% η=0.1%
20 141.9 141.2
25 143.9 143.5
31.5 139.7 138.8
40 138.2 137.3
50 136.72 135.6
63 135.9 134.7
80 134.3 133.1
100 133.4 132.1
125 132.9 131.6
160 131.3 129.9
200 129.8 128.5
250 128.4 127.2
315 127.3 126.1
400 125.0 123.8
500 123.7 122.6
630 121.6 120.5
800 119.5 118.4
1000 117.5 116.5
1250 115.3 114.5
1600 112.6 111.8
2000 110.2 109.5
2500 107.9 107.3
3150 105.7 105.1
4000 103.1 102.5
5000 100.6 100.1
6300 98.1 97.5
8000 95.4 94.8
Total sound pressure level 148.8 148.0
From Table 2, we can see that for the loss factor η=0.05%~0.1%, the sound pressure spectrum
level of noise of flow excited-vibration is about 148dB-149dB. Specifically, when η=0.05%, the
noise of flow excited-vibration is 149dB, and when η=0.1%, it’s 148dB.
3.3 Prediction of hydrodynamic noise (16kn)
The hydrodynamic noise can be determined by the superposition of the flow induced noise and
the noise of flow excited-vibration, and the results are shown in the Table 3. From the table, it’s
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clear to see that when η=0.05%, the sound pressure level of hydrodynamic noise it about 148.8dB;
while η=0.1%, the value is around 148.1dB.
Table 3 – Sound pressure spectrum level of hydrodynamic noise (dB)
Frequency, Hz η=0.05% η=0.1%
20 141.9 141.2
25 143.9 143.5
31.5 139.7 138.8
40 138.2 137.3
50 136.7 135.6
63 135.9 134.7
80 134.3 133.1
100 133.4 132.1
125 132.9 131.6
160 131.3 129.9
200 129.8 128.6
250 128.5 127.3
315 127.4 126.3
400 125.3 124.2
500 124.7 123.8
630 123.8 122.9
800 123.6 123.2
1000 128.1 128.0
1250 119.1 118.8
1600 115.6 115.2
2000 113.2 112.9
2500 112.2 111.9
3150 107.8 107.4
4000 104.9 104.5
5000 102.6 102.3
6300 100.3 99.95
8000 98.02 97.71
Total sound pressure level 148.8 148.1
It’s obvious that the hydrodynamic noise level of the frigate is 148dB~149dB. Considering the
uncertainty of the loss factor, the Sound pressure spectrum level of the hydrodynamic noise is in
the range of 148.1dB~148.8dB, which is a little lower compared to other ships with the same type.
So it can be drawn that the design of this frigate contributes to improving the stealth performance
and meets the design requirements.
4. CONCLUSIONS
In this paper, the hydrodynamic noise prediction analysis for one certain frigate at the speed of
16Kn is conducted. The flow induced noise and noise of flow induced-vibration are calculated
respectively by the separating prediction strategy. Firstly, the flow induced noise is studied by a
hybrid method of combining the FEM and BEM methods. The results show that the distribution of
the underwater sound field in the horizontal direction is more uniform and the flow induced noise
in the vertical direction plays the leading role. Then, the noise of flow excited-vibration is
determined using the SEA. In the analysis two extreme loss factors are considered. Lastly, the total
hydrodynamic noise is acquired by the stacking of the two component results, and it can be used
to evaluate whether the design of vehicles meets the requirements. The study of this paper can
provide the reference for the prediction of the hydrodynamic noise and the further noise reduction
to a degree.
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ACKNOWLEDGEMENTS
This paper is funded by the International Exchange Program of Harbin Engineering University
for Innovation-oriented Talents Cultivation. The works gratefully acknowledge the financial
support from the National Natural Science Foundation of China (Nos. 51209052), Heilongjiang
Province Youth Science Fund Project (Nos. QC2011C013) and Harbin Science and Technology
Development Innovation Foundation of youth (Nos. 2011RFQXG021). The works also
acknowledge the National Natural Science Foundation of China (No U1430236).
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