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 lvxiuhai@hrbeu.edu.cn 2 liangqian@hrbeu.edu.cn 3 shidongyan@hrbeu.edu.cn 4 wangqingshanxlz@hotmail.com

INTER-NOISE 2016

318

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

INTER-NOISE 2016

319

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

INTER-NOISE 2016

320

(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:

INTER-NOISE 2016

321

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

INTER-NOISE 2016

322

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

INTER-NOISE 2016

323

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).

INTER-NOISE 2016

324

(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）

INTER-NOISE 2016

325

(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

INTER-NOISE 2016

326

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.

INTER-NOISE 2016

327

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).

REFERENCES

1. Liu M, Ma Y. Analysis on hydrodynamic noise simulation around submarine fore region. SHIP

& OCEAN ENGINEERING. 2009;38(5):46-49.

2. Zhao J, Shi X, Du X. An integrated prediction method of torpedo flow noise. TORPEDO

TECHNOLOGY. 2009;17(2):10-14.

3. Heng Y, Yuan S, Hong F, Yuan J, Si Q, Hu B. A Hybrid Method for Flow-Induced Noise in

Centrifugal Pumps Based on LES and FEM. ASME 2013 Fluids Engineering Division Summer

Meeting. American Society of Mechanical Engineers, 2013: V01BT10A034-V01BT10A034.

4. Zhang Y, Fu H, Miao G. LES-based numerical simulation of flow noise for submerged body

with cavities. JOURNAL OF SHANGHAI JIAOTONG UNIVERSITY.

2011;45(12):1868-1873.

5. Jiang W, Zhang H, Meng K. Research on the flow noise of underwater submarine based on

boundary element method. Journal of Hydrodynamics. 2013;(004):453-459.

6. Durant C, Robert G, Filippi P J T, MATTEI P O. Vibroacoustic response of a thin cylindrical

shell excited by a turbulent internal flow: comparison between numerical prediction and

experimentation. Journal of sound and vibration. 2000;229(5):1115-1155.

7. Zhang N, Shen H, Yao H. Numerical simulation of cavity flow induced noise by LES and

FW-H acoustic analogy. Journal of Hydrodynamics, Ser. B. 2010;22(5):242-247.

8. Wei Y, Wang Y. Flow-excited submarine structure acoustic prediction based on a refined

integral algorithm. Chinese Journal of Computational Mechanics. 2012;29(4):574-581.

9. Wang K, Liu G, Wang Q, Zhang Y, Li X. Separating prediction of the hydrodynamic noise of

an underwater vehicle. Chinese Journal of Ship Research. 2015;10(4):29-38.

10. Jiang W. Numerical Simulation on Flow Noise and Flow-excited Noise of Submarine under

Fluid Structure Interaction. Shanghai: Shanghai Jiao Tong University, 2013.

11. Ross D. Mechanics of underwater noise. Elsevier, 2013.

12. Mellen R H. On modeling convective turbulence. The Journal of the Acoustical Society of

America. 1990;88(6):2891-2893.

INTER-NOISE 2016

328