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Study on prediction methods and characteristics of ship underwater radiated noise within full frequency
Ocean Engineering 174 (2019) 61–70
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Study on prediction methods and characteristics of ship underwater radiated noise within full frequency
T
Bo Zhanga,b, Yang Xianga,b,∗, Peng Hea,b, Guan-jun Zhanga,b a b
Key Laboratory of High Performance Ship Technology (Wuhan University of Technology), Wuhan, 430063, Ministry of Education, China School of Energy and Power Engineering, Wuhan University of Technology, Wuhan, 430063, China
ARTICLE INFO
ABSTRACT
Keywords: Full frequency Ship underwater radiated noise FE-BEM FE-IFEM FE-AML SEA Far field criterion
One trend in ship development is low noise characteristics. As one of the major noise sources of ship underwater radiated noise is the power equipment, it is critical to predict the ship underwater radiated noise caused by power equipment during the design phase. In this study, the incentive spectrums of power plants were obtained by testing on an oil tanker ship, and the hull vibration was calculated and measured in the middle and low frequency. The results show that the calculation model satisfies the accuracy requirement. To calculate the ship underwater radiated noise in the middle and low frequency, the finite element and boundary element method (FE-BEM), finite element and infinite element method (FE-IFEM), and finite element and automatic matching layer (FE-AML) were used, respectively. It is found that the FE-BEM is the preferred method for calculating ship underwater radiated noise in modeling scale and computational efficiency. The calculation of hull vibration and underwater radiated noise in the high frequency were performed by using the statistical energy analysis (SEA). Full frequency underwater radiated noise prediction of the oil tanker was completed. In the end, the far field of ship underwater sound radiation was studied. The far field can be determined when the sound radiation directivity of the ship no longer changes with distance.
1. Introduction During the voyage of a ship, its main power plants will cause vibration of the hull, which can induce the movement of the surrounding fluid to generate underwater acoustic radiation that may further cause adverse effects on marine organisms and damage the marine ecological balance (Nowacek D P et al., 2007; Williams R et al., 2015; Farcas A et al., 2015). In the past years, the subject of ship noise emission has been identified and the EU has funded the FP7 SILENV (Ship Innovative soLutions to rEduce Noise and Vibrations) project that runs from 2010 to 2012 (Borelli, D et al., 2016). In addition, for military ships, the most important indicator to measure the ship acoustic stealth performance is the ship underwater radiated noise level. The navies of various countries are currently vigorously developing sonar detection technology, which in turn has led to the acoustic stealth performance requirements of naval ships have become more stringent. The underwater noise forecast during the design stage can grasp the ship noise level in advance and provide the basis for the subsequent vibration and noise reduction design. The ship underwater noise sources usually have three types: mechanical noise, propeller noise, and hydrodynamic noise, among which the mechanical noise and propeller noise are the most important. There are various studies have investigated the ship underwater radiated noise caused by ∗
the propeller. Gaggero S et al. (2016) dealt with the side effects of propellers cavitation, i.e. pressure pulses and radiated noise. They presented a survey of a specific test case represented by a single-screw research vessel in the framework of the project AQUO (Achieve QUieter Oceans by shipping noise footprint reduction), which was analyzed with three different strategies: numerical calculations, model scale investigations, and full-scale measurements. Seol H et al. (2005) used a time-domain acoustic analogy to calculate underwater propeller noise, the potential-based panel method was used to analyze the flow field, and then the pressure and other data in the time domain was substituted into the Ffowcs-Williams and Hawkings (FWH) equation to calculate the ship underwater far field radiated noise. Kellett P et al. (2013) and Özden M C et al. (2016) adopted CFD software and Ffowcs-Williams and Hawkings (FWH) equation to calculate ship underwater radiated noise generated by propeller under different flow conditions and discussed the improvement of the calculation method. Lidtke A K et al. (2016) further studied the modeling methods of propeller and cavitation model, and the cavitation induced noise was calculated by Large Eddy simulation and FWH acoustic analogy. The calculation of propeller radiated noise has been relatively mature. This study mainly focuses on the ship underwater radiated noise caused by the power plants. However, not only the structure of a ship is complicated, but also the excitation is complex. In addition, only the
Corresponding author. Key Laboratory of High Performance Ship Technology (Wuhan University of Technology), Wuhan, 430063, Ministry of Education, China. E-mail address: [email protected] (Y. Xiang).
https://doi.org/10.1016/j.oceaneng.2019.01.028 Received 2 May 2018; Received in revised form 30 November 2018; Accepted 9 January 2019 0029-8018/ © 2019 Elsevier Ltd. All rights reserved.
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numerical method is available for solving its vibration and radiated noise. There are various numerical methods for calculating underwater vibration and radiated noise of complex structure, such as finite element method (FEM), boundary element method (BEM), wave superposition method (WSM), infinite element method (IFEM), automatic matching layer (AML), statistical energy analysis (SEA) and finite element-statistical energy analysis hybrid method (FE-SEA) (Xiang Y, 2017; Wu S W, 2018; Zhou M S et al., 2017). Tang Z Y (2011) and Peng X (2003) applied FE-BEM to calculate the ship underwater radiated noise in the middle and low frequency, and obtained good results. Qiu Z H, Liu S et al. (2013) used the IFEM to calculate the low frequency underwater radiated noise of the ship and studied the influence of damping on the underwater radiated noise. In high-frequency region, structures usually exhibit short wave and high modality characteristics. In order to calculate the structure high frequency acoustic and vibration response, statistical energy analysis (SEA) was proposed (Yao D Y et al., 1995; Morrow C T, 2013). Liu K et al. (2010) and Li X M et al. (2013) used SEA to predict the ship underwater radiated noise, and the results showed that the SEA can be well applied to the calculation of high frequency vibration and radiated noise of ship. However, there are still deficiencies in the prediction of ship underwater radiated noise caused by power plants. ① In the middle and low frequency region, FE-BEM or FE-IFEM has been used to calculate the ship underwater radiated noise. It is rare to use different methods to calculate the ship underwater radiated noise and compare the calculation methods’ differences. ② There are few comparisons between the hull vibration measured values and simulation values. ③ There is less research on the far field criteria of ship underwater acoustic radiation. In this study, an oil tanker was used to study the full frequency underwater radiated noise by different numerical methods, and the method for judging ship acoustic radiation far field was developed. The flow diagram of this study is shown in Fig. 1.
divided by N ≤ 1, 1 < N < 5, and N ≥ 5, respectively. (Yao D Y et al., 1995). The modal number N is calculated according to the narrowband spectrum, and then the integral operation is performed according to the upper and lower limits of the octave. The 1/3 octave is chosen to calculate the oil tanker substructures, modal number N to reduce the calculation scale, but this does not affect the division result of the frequency band. The modal number N of the hull structures were calculated based on equation (1) ∼ (3) and plotted in Fig. 2. According to the modal numbers of the different hull structure subsystems in Fig. 2, the low, middle, and high frequency regions of ship underwater radiated noise calculation can be divided as 20–50 Hz (less than 1 below 50 Hz), 50–200 Hz, and 200–8000 Hz (greater than 5 above 200 Hz), respectively. 2.2. Vibration wet mode calculation and harmonic response analysis The ship is sailing in an infinite fluid domain, the coupling with the surrounding fluids should be taken into consideration. The hull structure vibration characteristics in vacuum can be expressed by the Norder matrix differential equation (Li, 2016): where, M、C 、K are the hull structures mass, damping and stiffness ¨ are the hull structures vibration dismatrices respectively, X 、X 、X placement, velocity, and acceleration matrices respectively, Ft is the excitation load. Considering the fluid coupling effect, equation (4) can be rewritten as where, Fw = RTp , R is the coupling matrix, and p is the node sound pressure vector. The relationship between R and p is obtained by equation (6): where, Mw 、Kw 、C w are the fluid mass, stiffness, and damping matrices respectively, p is the first derivative of the node sound pressure vector, p¨ is the second derivative of the node sound pressure vector, and is the seawater density. The differential equation of hull-fluid coupling vibration matrix can be obtained by combining equations (5) and (6):
To calculate ship underwater radiated noise, different methods should be used for different analysis frequency bands. Therefore, dividing the frequency interval reasonably is important in calculating the ship underwater radiated noise within the full frequency. The modal number N has often been used to divide the frequency band (Yao D Y et al., 1995), which can be calculated by
M 0 R Mw
1
[ 2
A 14 ] EI
M 0 R Mw
3A hCl
+
C 0 0 Cw
X p
+
K 0
RT Kw
{ Xp } = {F0 } t
(7)
¨ X p¨
+
K 0
RT Kw
{ Xp } = {0}
(8)
The ship vibration wet mode can be obtained by solving equation (8). The study object is an offshore oil tanker with a total length of 101.60 m, as shown in Fig. 3. Based on the ship drawings, the oil tanker and fluid finite element models were established and the fluid-structure interaction (FSI) was used to define the fluid-structure coupling surface between the hull wet surface and the fluid, as shown in Fig. 4. The asymmetric method was used to calculate the ship vibration wet mode. The first 200 steps were extracted and the frequency range was 0–200 Hz. Among the obtained mode results, only the four overall modes are found, as shown in Fig. 5, and the rest are hull partial modes. The natural frequencies of the first 2 orders of the overall vertical vibration of the ship were estimated based on the ship type parameters and Todd's formula (F. H. Todd, 1948). The estimated results are shown in Table 1, the Todd's formula is:
(2)
where, is the frequency, A is the cross-sectional area of the beam structure, is the mass density, EI is the structural bending stiffness. The modal density of two-dimensional flat structure can be got by
n( ) =
¨ X p¨
Considering that the hull is undamped free vibration, equation (7) can be rewritten as
(1)
where, n ( ) is the structure modal density and f is the frequency bandwidth. The modal density is an important parameter to measure the storage capacity of subsystem vibration energy. According to the statistical energy theory, when the modal density of the substructure is larger, the modality of the substructure within the bandwidth is more dense, and the calculation result has statistical significance. The modal density of one-dimensional beam structure can be got by
1
(6)
¨ =0 Mw p¨ + C w p + Kw p + RX
2.1. Frequency band division
n( ) =
(5)
¨ + CX + KX = Ft + Fw MX
2. Middle and low frequency underwater radiated noise prediction of an oil tanker
N = n( ) f
(4)
¨ + CX + KX = Ft MX
(3)
where, h and A are the thickness and area of plate structure respectively, Cl is the structure bending wave velocity. In engineering, the low, middle, and high frequency regions are
Nv1 = 0.0167( 62
BDe3 + ) 3 VL
(9)
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Prediction of ship underwater radiated noise within full frequency
Frequency interval division
Middle and low frequency region
High frequency region
Hull vibration calculation
Acoustic and vibration coupling calculation
Hull vibration measurement
revise
bad
Realize the calculation of the ship underwater radiated noise within full frequency
Calculation accuracy evaluation
good
Hull underwater radiated noise calculation
FE-BEM
FE-IFEM
Far field criteria of ship underwater acoustic radiation
FE-AML
Comparison of calculation methods
Recommended method
Fig. 1. The flow diagram of prediction.
Fig. 3. Real ship of prediction. Fig. 2. Modal numbers of the hull structures.
where, , are ship type correction factor, for oil tanker: = 94900, = 28, V is the total mass of the ship including the surrounding seawater, V = 12933.8t, B is the ship type width, B = 14.2 m, De is the ship equivalent type deep, De = 7.5m, L is the ship vertical line length, L = 95.6 m. The Todd's formula is used to calculate the natural frequency of the first-order overall vertical vibration, and the natural frequency of the second-order vertical vibration is given by
Nv 2 = CNv1
Fig. 4. Fluid-structure interaction model and fluid-structure coupling surface (red area).
(10)
fH = (BH KH
where, C is a dimensionless coefficient, C = 2.02 . The formula for estimating the horizontal vibration mode is: 63
IH 3 HL
+ AH ) × 0.0167
(11)
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Fig. 5. The overall vibration wet mode of the ship. Table 1 The ship overall vibration mode natural frequency Hz. Order
Simulation value
Estimated value
Vibration mode
Relative error/%
1 2 3 4
1.646 1.838 3.062 4.205
1.622
First-order vertical First-order horizontal Second-order vertical Second-order horizontal
1.480
3.288
where, fH is the first horizontal vibration natural frequency, Hz; AH , BH are ship type correction factors; IH is the moment of inertia of the ship vertical axis, m4; H is the total mass of the hull and the attached seawater, t; L is the length between the hull vertical lines, m; KH is the correction coefficient of the hull profile moment of inertia. Since there is a lack of IH , the estimated value of the hull first horizontal vibration is temporarily unavailable. In engineering, the overall vertical vibration of the hull is more concerned as it has the greatest impact on the acoustic and vibration response of the ship (Weng C J, 1985). In Fig. 5, the oil tanker overall vibration mode can be divided into two major categories: vertical vibration mode and horizontal vibration mode, which appear alternately. The twisting or torsional modes usually occur in ships with large openings in the deck, such as container ships. From Table 1, the error is within 10% of the simulation values and estimated values of the first 2 vertical overall vibration natural frequency, which shows that the simulation model is credible. Through the study of the overall vibration of the hull, the basic dynamic characteristics of the ship can be more effectively grasped. The excitation frequency of the hull can be staggered from the natural frequency at the design stage, thus avoiding the occurrence of the overall resonance of the hull, which is of great significance in improving the quality and service life of the ship. Only the underwater radiated noise caused by the power plants is considered in this paper. The hull vibration response under the excitation of the main power plants was calculated. The main power
6.873
plants in the engine room include the main diesel engine, gearbox and diesel generator unit, the power plants specific parameters are shown in Table 2 and Table 3. The foot vibration accelerations of the power plants were obtained through real ship testing. Considering the test instruments, the sampling frequency is set to 16 kHz and the sampling time is set to 2 s. The measurement site is shown in Fig. 6, and the measured results are shown in Fig. 7. In engineering, the calculation of ship acoustic and vibration response is usually carried out under 1/3 octave. To study the ship underwater radiated noise characteristics of the middle and low frequency more accurately, normal spectrum density is chosen in middle and low frequency. The calculation frequency range is 20–200 Hz and the frequency interval is 2 Hz. The vibration acceleration test was performed on the local parts of the oil tanker and compared with the simulation results. The comparison results are shown in Fig. 8. The simulation overall values and Table 2 Main engine basic parameters.
64
Type
6DKM-26
Rated power Pe/kW Rated speed ne/(r/min) Number of cylinders Nc Mass/t Amount
1618 750 6 18.0 1
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Table 3 Diesel generator unit basic parameters. Type
Generator (DKBH4320/06)
Diesel engine (R6160ZC)
Rated power Pe/kW Rated speed ne/(r/min) Mass/kg Amount
160 1000 780 2
200 1000 940 2
Table 4 Comparison of simulation overall values and measured overall values in the bandwidth dB.
| t=1
At
Ft At
|
Error
Full spectrum MAPE
Engine room bulkhead Upper deck Upper deck side Poop deck Poop deck front wall Ship's cab
102.9
102.1
0.8
4.8%
79.3 102.5 82.7 73.9
77.8 96.3 83.9 70.5
1.5 6.2 1.2 3.4
14.6% 10.6% 12.0% 12.6%
86.7
88.3
1.6
16.0%
The BEM, IFEM, and AML are common numerical methods for calculating structure radiated noise in the middle and low frequency. The BEM combines classical integral equations and finite element theory. The integral equation may be regarded as an exact solution of the governing partial differential equation. The BEM attempts to use the given boundary conditions to fit boundary values into the integral equation. Once this is done, in the post-processing stage, the integral equation can be used again to calculate numerically the solution directly at any desired point in the interior of the solution domain. The infinite element method is a modification of the finite element method. The method divides the domain concerned into infinitely many sections. The structure of the acoustic IFEM is composed of two parts: the finite inner region of the envelope structure model and the semiinfinite outer region. The limited inner region is dispersed by finite elements, the semi-infinite outer region is dispersed by divergent infinite elements, and the nodes are coupled at the interface to ensure continuity in the process of outward propagation of sound pressure. The AML is a new type of finite element method. The calculation principle is to artificially set a finite thickness medium layer to absorb sound waves at the acoustic finite element boundary. The absorption layer makes sound waves decay rapidly in exponential form. Therefore, the sound wave at the boundary of the medium layer is substantially zero. There are also differences among the three methods. The BEM requires a surface mesh, but the IFEM and the AML require a volume mesh of the external sound field. Three methods are also different in acoustic boundary processing. The BEM directly takes the vibration displacement of the hull as the acoustic boundary condition, but the IFEM and the AML not only use the vibration displacement as the boundary condition, but also assign the infinite element attribute and the matching layer attribute respectively to the external sound field boundary. The BEM, IFEM, and AML were used to calculate the middle and low frequency underwater radiated noise of the oil tanker respectively. The differences in the modeling scale, computational accuracy and computational time-consuming of the three methods were explored. The calculated frequency band was 20–200 Hz with 2 Hz interval. It should be noted that the ship has a free liquid surface. In the BEM, the free liquid surface is simulated by setting anti-symmetric boundary condition, but in the IFEM and AML, the air impedance is defined at the free liquid surface. The acoustic boundary and free liquid surface processing of three methods are shown in Fig. 9. The calculated result of the oil tanker radiated sound power is shown in Fig. 10. In Fig. 10, in the range of 20–170 Hz, the radiated sound power curves obtained from the three methods agree well with each other. In the range of 170–200 Hz, the radiated sound power obtained by the FEBEM is slightly larger in amplitude than that of the FE-IFEM and FE-
measured overall values obtained by synthesizing the vibration acceleration in the bandwidth are shown in Table 4. From Fig. 8, the vibration calculation values of each measuring point have a good consistency with the measured values. The difference in amplitude is caused by factors, such as modeling error and neglect of other auxiliary mechanical equipment incentives. In Table 4, the maximum error between the simulation values and the measured values of the overall vibration acceleration level is 6.2 dB. The mean absolute percentage error (MAPE) is a measure of prediction accuracy of a forecasting method in statistics, and is defined by the formula: n
Measured value
2.3. Middle and low frequency underwater radiated noise calculation of oil tanker
Fig. 7. Frequency-domain vibration acceleration of main engine, gearbox and diesel generator unit.
100% n
Simulation value
engineering requirements and the hull vibration simulation values have good reliability and accuracy.
Fig. 6. Power plants acceleration measurement site (main diesel engine, gearbox, and diesel generator unit).
M=
Measuring point
(12)
where, At is the measured value, Ft is the simulation value. The MAPE for each one of the measuring points was calculated by using every frequency value of the spectra between 20 and 200 Hz. The full spectrum MAPEs of these measuring points are shown in Table 4. The maximum MAPE value is 16.0%, which satisfies the general
Fig. 8. Comparison of simulated and measured values for some measuring points. 65
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Anti-symmetric boundary
Vibration mapping surface
Vibration mapping surface Free liquid surface
Free liquid surface
IFEM
Fig. 9. BEM, IFEM, and AML acoustic boundary and free liquid surface processing.
AML
radiated noise. For example, the acoustic finite element boundary must be drawn as an ellipse or a sphere, and the infinite element layer thickness must satisfy 1–2 acoustic wavelengths, which will result in an increase in the number of model meshes and a reduction in computational speed. At the same time, the calculation accuracy of IFEM is related to the chosen order. Higher orders ensure high computational accuracy, but also result in poor convergence of the numerical solution. AML has no specific requirements for the boundary shape of the acoustic finite element and the thickness of the finite element layer. The acoustic calculation element numbers are much less than the IFEM, and the calculation efficiency is higher. Compared to BEM, AML needs to divide the sound field model into a volume mesh. For large models such as ships, the number of sound field grids is usually more, but BEM only needs to extract the wet surface grid of the hull structure. The BEM calculation speed is better than AML. Therefore, in engineering, the FEM-BEM method is recommended for ship underwater radiated noise calculation in the middle and low frequency. The differences in the modeling scale, computational accuracy and computational time-consuming of the three methods are shown in Table 5. The coefficient matrix of the linear equations formed by the traditional BEM is an asymmetric dense matrix, which leads to its shortcomings of high computation and high memory consumption. According to engineering experience, when the boundary element model degree of freedom N exceeds 15000, the traditional BEM will consume a lot of computer resources and a long solution time. Fast multipole BEM replaces the direct connection between the source point and the field point with the indirect connection by introducing the multipole expansion of the kernel function. The interaction between particles is replaced with the interaction between set elements. The fast multipole algorithm speeds up the multiplication of matrix and vector, and reduces the computation and memory consumption from O(N)3 to O(N), which increases the solution speed.
Fig. 10. The underwater radiated sound power of the ship.
AML. However, the calculation results of the three methods still maintain a good consistency in the trend. The overall underwater radiated sound power levels of oil tankers obtained from FE-BEM, FEIFEM, and FE-AML are 139.0 dB, 135.4 dB, and 135.8 dB respectively, and the maximum difference is 3.6 dB. Most of the sound power peak frequencies are consistent with the excitation of the power plants. Peaks at other frequencies, such as 112 Hz and 120 Hz, may be related to the vibration transmission path and the impedance characteristics of the radiated medium. The structure acoustic radiated characteristics are not only related to the excitation source, but also related to the transmission path and the radiated medium. The radiated sound pressure cloud pictures of the field points obtained by the three methods are shown in Fig. 11. In Fig. 11, at different frequencies, the radiated sound pressure levels near the excitation source are relatively large. At 22 Hz, the sound radiation of the oil tanker is mainly manifested as overall radiation, and as the frequency increases, the sound radiation gradually becomes local radiation. There are discrepancies in sound pressure distribution among the three methods, which may be due to several reasons: ① BEM calculates the sound pressure of the external sound field by surface mesh integration, while AML and IFEM calculate the sound pressure of the external sound field by volume mesh integration.② The three methods are different in boundary processing. ③ In the BEM, the free liquid surface is simulated by setting anti-symmetric boundary condition, but in the IFEM and AML, the air impedance is defined at the free liquid surface. To study the sound pressure levels of certain specific locations, three different field points are established respectively at the horizontal 100 m on the ship both sides and 100 m underwater at the center of the ship bottom. The sound pressure levels of these field points were calculated and the results are shown in Fig. 12. In Fig. 12, the radiated sound pressure spectrums are basically consistent with the ship radiated sound power spectrum, the sound pressure peak frequencies are basically the same. In the range of 20–200 Hz, the radiated sound pressure level curves obtained by the three methods agree well with each other. The sound pressure level in the ship vertical direction is greater than the horizontal direction sound pressure level at the same distance. IFEM has many limitations in the calculation of ship underwater
3. High frequency underwater radiated noise prediction for oil tanker In the high frequency region, the statistical energy method was used to calculate the ship underwater radiated noise. The SEA is a statistical method in space and frequency domain, which takes energy as a variable. Under the premise of satisfying the modal density requirement, it is of practical significance to using the SEA to predict the high frequency underwater vibration and noise of ships. The energy balance equation of a conservative acoustic-structure weakly coupled system consisting of N subsystems is (Yao D Y et al., 1995):
E ( ) = Pin ( )
(13)
where, is the frequency, is the system coupling loss factor matrix, E( ) is the subsystem energy matrix, and Pin ( ) is the subsystem input power matrix. In the high frequency, the structure radiated sound power is (Yao D Y et al., 1995):
Pr = R
2
(14)
where, R is the real part of the structure radiated sound impedance, is the hull mean square vibration velocity.
R= 66
r
M
2
(15)
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FE-BEM
FE-AML
FE-IFEM
(a) 22 Hz
(b) 48 Hz
(c) 100 Hz
Fig. 11. The underwater radiated sound pressure cloud pictures of the ship.
velocity cloud pictures are shown in Fig. 15. In Fig. 15, the hull vibration velocity near the excitation source is the largest. As the distance increases, the vibration velocity of the hull gradually decreases. From the viewpoint of the amplitude, as the frequency increases, the vibration velocity of the hull structure becomes smaller gradually. The mathematical average of the radiated sound power of the field points at three different locations are shown in Fig. 16. The radiated sound pressure levels of the three field points in the model are shown in Fig. 17, where field point 1 and field point 3 are the semi-infinite fluids on both sides of the ship and the field point 2 is the ship bottom semi-infinite fluid. In Fig. 16, the radiated sound power of the oil tanker in the range of
Fig. 12. The field points radiated sound pressure at the left, right sides and the bottom of the ship. Table 5 The differences between the three methods. Methods
Modeling scale
Computational accuracy
Time-consuming/ h
FE-BEM FE-AML FE-IFEM
small medium large
good good medium (relate to the chosen order)
3.5 8.0 11.5
where, r is the acoustic radiated loss factor, is the frequency and M is the structure mass matrix. In the high frequency band (200–8000 Hz), if the normal spectrum density is also selected to calculate ship underwater vibration and radiated noise, this would lead to a sharp increase in the number of calculation frequency points and a sharp increase in the calculation scale. Generally, there are enough frequency points between 200 and 8000 Hz in 1/3 octave to reflect the ship high frequency acoustic and vibration characteristics. The statistical energy model of the oil tankers is established, as shown in Fig. 13. The measured vibration acceleration levels of the power plants are shown in Fig. 14. The calculated frequency range is 200–8000 Hz at 1/3 octave frequency. The calculated hull vibration
Field Point 1 Field Point 3 Field Point 2 Fig. 13. The ship statistical energy model. 67
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Fig. 14. The vibration acceleration level of the power plants.
Fig. 16. Radiated sound power of oil tanker.
200–800 Hz increases slowly with frequency increasing. In the range of 800–4000 Hz, the radiated sound power starts to decrease with frequency increasing. After 4000 Hz, the radiated sound power starts to rise slowly again. In Fig. 17, the variation trend of the radiated sound pressure level curve of the three field points is basically the same as the radiated sound power curve. The field point 1 and the field point 3 are geometrically symmetrical, but the radiated sound pressure level at the field point 3 is greater than that at the field point 1 due to the fact that only the starboard diesel generator is turned on in the actual sailing condition. 4. Study on the far-field criterion of underwater acoustic radiation of ship The ship underwater radiation sound field has far field and near field, and the sound pressure has large fluctuations in the near field. For general sound sources, the radiated sound pressure decreases with distance in the far field. For a structure sound source, the sound pressure satisfies the following conditions in the far field.
P (r , , ) =
Pequ ( ,
Fig. 17. The sound pressure level of semi-infinite field point.
)
(16)
r
(r , , ) =
where, r is the distance from the field point to the equivalent sound source, and Pequ is the equivalent sound pressure amplitude, is the azimuth angle, is the elevation angle. The far-field sound pressure directivity function is
a
200 Hz
Pequ ( , ) max[Pequ ( , )/r ] r
=
Pequ ( , ) max[Pequ ( , )]
(17)
So the far-field radiation sound pressure directivity function is not related to r . The far field location can be determined when the ship
b 2000 Hz Fig. 15. The vibration cloud pictures at different frequencies of the ship. 68
c
8000 Hz
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Fig. 18. The sound pressure directivity of the ship.
sound radiation directivity does not change with distance. The 50 m below the center of geometry of the ship is taken as the center, four different planes of sound radiation directivity parallel to the XY plane (horizontal middle section) were established with a radius of 30 m, 50 m, 80 m, and 100 m. The BEM was used to calculate the underwater sound pressure directionality of the ship, and the results are shown in Fig. 18. The 0°, 90°, 180° and 270° respectively represent the bow, the port side, the poop, and the starboard side of the oil tanker. In Fig. 18, at all given frequencies, when the horizontal radiation radius reaches 80 m, the number of radiated sound pressure directivity side lobes no longer changes, and the directivity change laws are basically the same. In other words, after the radius of radiation reaches 80 m, the directivity of the ship radiated sound pressure no longer changes with distance. Therefore, for the oil tanker, at the underwater depth of 50 m, when the horizontal radiation radius reaches 80 m, it is already the far field of the ship underwater sound radiation.
method are reliable, and the peak frequencies of the vibration response of the hull are mostly consistent with the peak frequencies of the excitation sources. (2) The radiated sound power and sound pressure of the oil tanker obtained by the three different calculation methods are relatively consistent. Based on the analysis, FE-BEM shows a smaller modeling scale, better calculation accuracy and shorter solution time. (3) Using ship sound radiation directivity as a far-field criterion method is relatively intuitive. The far-field location of sound radiation can be determined when the sound radiation directivity no longer changes with distance. Acknowledgment This work was supported by the National Nature Science Foundation of China-P. R .China (Grant Nos. 51079118/5129148) and Defense Preresearch Project of China-P. R .China (Grant Nos. 10204010410).
4. Conclusion
References
For a certain type of oil tanker, this study firstly compares the hull vibration simulation results with the experimental results to validate the ship calculation model. Then, the FE-BEM, FE-AML, and FE-IFEM were used to calculate the middle and low frequency underwater radiated noise of the oil tanker, respectively. The differences among the three methods were explored in the modeling scale, calculation accuracy, and calculation expensiveness. The SEA was used to calculate the high frequency vibration and underwater radiated noise of the oil tanker, so that the full frequency underwater radiated noise calculation and characteristics research of the oil tanker were realized. Last, the ship sound radiation far-field criterion was studied based on sound radiation directivity. The main conclusions are summarized as follows:
Borelli, D., Gaggero, T., Rizzuto, E., et al., 2016. Holistic control of ship noise emissions. Noise Mapp. 3 (1), 107–119. Farcas, A., Thompson, P.M., Merchant, N.D., 2016. Underwater noise modelling for environmental impact assessment. Environ. Impact Assess. Rev. 57, 114–122. Gaggero, S., Gaggero, T., Rizzuto, E., et al., 2016. Ship propeller side effects: pressure pulses and radiated noise. Noise Mapp. 3 (1), 295–315. Kellett, P., Turan, O., Incecik, A., 2013. A study of numerical ship underwater noise prediction. Ocean. Eng. 66 (3), 113–120. Li, Y.L., 2016. Research on Propeller-Induced Ship Hull Vibration and Underwater Radiated Noise. Harbin Engineering University, Haerbing. Li, X.M., Weng, Z.Z., 2013. Underwater Radiated Noise Calculation Based on Statistical Energy Analysis Method [C]//Ship Underwater Noise Symposium. Lidtke, A.K., Humphrey, V.F., Turnock, S.R., 2016. Feasibility study into a computational approach for marine propeller noise and cavitation modelling. Ocean. Eng. 120, 152–159. Liu, K., Zhu, S.J., Ding, S.C., 2010. Prediction method of radiation noise of Torpedo structure based on AutoSEA. Torpedo Technology 18 (2), 91–94. Morrow, C.T., 2013. Statistical energy analysis of dynamical systems: theory and applications, by Richard H. Lyon. Nano Lett. 13 (3), 917–924.
(1) The oil tanker vibration calculated values agree well with the measured values. The simulation model and vibration calculation 69
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B. Zhang et al. Nowacek, D.P., Thorne, L.H., Johnston, D.W., et al., 2007. Responses of cetaceans to anthropogenic noise. Mamm Rev. 37 (2), 81–115. Özden, M.C., Gurkan, A.Y., Ozden, Y.A., et al., 2016. Underwater radiated noise prediction for a submarine propeller in different flow conditions. Ocean. Eng. 126, 488–500. Peng, X., Luo, D.P., 2003. Ship structure modeling and prediction of underwater vibration and radiating noise. Noise and Vibration Control 23 (6), 9–12. Qiu, Z.H., Liu, S., Zheng, L., et al., 2013. Influence of damping on the underwater acoustic radiation characteristics of the ship Structure based on IFEM. SHIP & BOAT 24 (1), 40–44. Seol, H., Suh, J.C., Lee, S., 2005. Development of hybrid method for the prediction of underwater propeller noise. J. Sound Vib. 288 (1–2), 345–360. Tang, Z.Y., 2011. Research on Underwater Noise Prediction and Technology of Vibration and Noise Reduction of Survey Ship. Jiangsu University of Science and Technology, Zhenjiang.
Todd, F.H., 1948. Ship Vibration. The North East Coast Institution of Engineers and Shipbuilders, London. Weng, Chang-jian, 1985. Hull Vibration. China Communications Press, Beijing. Williams, R., Wright, A.J., Ashe, E., et al., 2015. Impacts of anthropogenic noise on marine life: publication patterns, new discoveries, and future directions in research and management. Ocean Coast Manag. 115, 17–24. Wu, S.W., Xiang, Y., et al., 2018. A meshfree radial point interpolation coupled with infinite acoustic wave envelope element method for computing acoustic fields. Acta Acustica united Acustica 104 (1), 64–78. Xiang, Y., 2016. Research status and development of radiation noise prediction and structure acoustic optimization. Ship & Ocean Eng. 45 (1), 71–77. Yao, D.Y., Wang, Q.Z., 1995. The Principle of Statistical Energy Analysis and its Application. Beijing Institute of Technology Press, Beijing. Zhou, M.S., Wu, Y.S., 2017. Sono-elasticity of Ships and the related applications. Adv. Mech. 47 (1), 385–428.
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Study on prediction methods and characteristics of ship underwater radiated noise within full frequency
T
Bo Zhanga,b, Yang Xianga,b,∗, Peng Hea,b, Guan-jun Zhanga,b a b
Key Laboratory of High Performance Ship Technology (Wuhan University of Technology), Wuhan, 430063, Ministry of Education, China School of Energy and Power Engineering, Wuhan University of Technology, Wuhan, 430063, China
ARTICLE INFO
ABSTRACT
Keywords: Full frequency Ship underwater radiated noise FE-BEM FE-IFEM FE-AML SEA Far field criterion
One trend in ship development is low noise characteristics. As one of the major noise sources of ship underwater radiated noise is the power equipment, it is critical to predict the ship underwater radiated noise caused by power equipment during the design phase. In this study, the incentive spectrums of power plants were obtained by testing on an oil tanker ship, and the hull vibration was calculated and measured in the middle and low frequency. The results show that the calculation model satisfies the accuracy requirement. To calculate the ship underwater radiated noise in the middle and low frequency, the finite element and boundary element method (FE-BEM), finite element and infinite element method (FE-IFEM), and finite element and automatic matching layer (FE-AML) were used, respectively. It is found that the FE-BEM is the preferred method for calculating ship underwater radiated noise in modeling scale and computational efficiency. The calculation of hull vibration and underwater radiated noise in the high frequency were performed by using the statistical energy analysis (SEA). Full frequency underwater radiated noise prediction of the oil tanker was completed. In the end, the far field of ship underwater sound radiation was studied. The far field can be determined when the sound radiation directivity of the ship no longer changes with distance.
1. Introduction During the voyage of a ship, its main power plants will cause vibration of the hull, which can induce the movement of the surrounding fluid to generate underwater acoustic radiation that may further cause adverse effects on marine organisms and damage the marine ecological balance (Nowacek D P et al., 2007; Williams R et al., 2015; Farcas A et al., 2015). In the past years, the subject of ship noise emission has been identified and the EU has funded the FP7 SILENV (Ship Innovative soLutions to rEduce Noise and Vibrations) project that runs from 2010 to 2012 (Borelli, D et al., 2016). In addition, for military ships, the most important indicator to measure the ship acoustic stealth performance is the ship underwater radiated noise level. The navies of various countries are currently vigorously developing sonar detection technology, which in turn has led to the acoustic stealth performance requirements of naval ships have become more stringent. The underwater noise forecast during the design stage can grasp the ship noise level in advance and provide the basis for the subsequent vibration and noise reduction design. The ship underwater noise sources usually have three types: mechanical noise, propeller noise, and hydrodynamic noise, among which the mechanical noise and propeller noise are the most important. There are various studies have investigated the ship underwater radiated noise caused by ∗
the propeller. Gaggero S et al. (2016) dealt with the side effects of propellers cavitation, i.e. pressure pulses and radiated noise. They presented a survey of a specific test case represented by a single-screw research vessel in the framework of the project AQUO (Achieve QUieter Oceans by shipping noise footprint reduction), which was analyzed with three different strategies: numerical calculations, model scale investigations, and full-scale measurements. Seol H et al. (2005) used a time-domain acoustic analogy to calculate underwater propeller noise, the potential-based panel method was used to analyze the flow field, and then the pressure and other data in the time domain was substituted into the Ffowcs-Williams and Hawkings (FWH) equation to calculate the ship underwater far field radiated noise. Kellett P et al. (2013) and Özden M C et al. (2016) adopted CFD software and Ffowcs-Williams and Hawkings (FWH) equation to calculate ship underwater radiated noise generated by propeller under different flow conditions and discussed the improvement of the calculation method. Lidtke A K et al. (2016) further studied the modeling methods of propeller and cavitation model, and the cavitation induced noise was calculated by Large Eddy simulation and FWH acoustic analogy. The calculation of propeller radiated noise has been relatively mature. This study mainly focuses on the ship underwater radiated noise caused by the power plants. However, not only the structure of a ship is complicated, but also the excitation is complex. In addition, only the
Corresponding author. Key Laboratory of High Performance Ship Technology (Wuhan University of Technology), Wuhan, 430063, Ministry of Education, China. E-mail address: [email protected] (Y. Xiang).
https://doi.org/10.1016/j.oceaneng.2019.01.028 Received 2 May 2018; Received in revised form 30 November 2018; Accepted 9 January 2019 0029-8018/ © 2019 Elsevier Ltd. All rights reserved.
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numerical method is available for solving its vibration and radiated noise. There are various numerical methods for calculating underwater vibration and radiated noise of complex structure, such as finite element method (FEM), boundary element method (BEM), wave superposition method (WSM), infinite element method (IFEM), automatic matching layer (AML), statistical energy analysis (SEA) and finite element-statistical energy analysis hybrid method (FE-SEA) (Xiang Y, 2017; Wu S W, 2018; Zhou M S et al., 2017). Tang Z Y (2011) and Peng X (2003) applied FE-BEM to calculate the ship underwater radiated noise in the middle and low frequency, and obtained good results. Qiu Z H, Liu S et al. (2013) used the IFEM to calculate the low frequency underwater radiated noise of the ship and studied the influence of damping on the underwater radiated noise. In high-frequency region, structures usually exhibit short wave and high modality characteristics. In order to calculate the structure high frequency acoustic and vibration response, statistical energy analysis (SEA) was proposed (Yao D Y et al., 1995; Morrow C T, 2013). Liu K et al. (2010) and Li X M et al. (2013) used SEA to predict the ship underwater radiated noise, and the results showed that the SEA can be well applied to the calculation of high frequency vibration and radiated noise of ship. However, there are still deficiencies in the prediction of ship underwater radiated noise caused by power plants. ① In the middle and low frequency region, FE-BEM or FE-IFEM has been used to calculate the ship underwater radiated noise. It is rare to use different methods to calculate the ship underwater radiated noise and compare the calculation methods’ differences. ② There are few comparisons between the hull vibration measured values and simulation values. ③ There is less research on the far field criteria of ship underwater acoustic radiation. In this study, an oil tanker was used to study the full frequency underwater radiated noise by different numerical methods, and the method for judging ship acoustic radiation far field was developed. The flow diagram of this study is shown in Fig. 1.
divided by N ≤ 1, 1 < N < 5, and N ≥ 5, respectively. (Yao D Y et al., 1995). The modal number N is calculated according to the narrowband spectrum, and then the integral operation is performed according to the upper and lower limits of the octave. The 1/3 octave is chosen to calculate the oil tanker substructures, modal number N to reduce the calculation scale, but this does not affect the division result of the frequency band. The modal number N of the hull structures were calculated based on equation (1) ∼ (3) and plotted in Fig. 2. According to the modal numbers of the different hull structure subsystems in Fig. 2, the low, middle, and high frequency regions of ship underwater radiated noise calculation can be divided as 20–50 Hz (less than 1 below 50 Hz), 50–200 Hz, and 200–8000 Hz (greater than 5 above 200 Hz), respectively. 2.2. Vibration wet mode calculation and harmonic response analysis The ship is sailing in an infinite fluid domain, the coupling with the surrounding fluids should be taken into consideration. The hull structure vibration characteristics in vacuum can be expressed by the Norder matrix differential equation (Li, 2016): where, M、C 、K are the hull structures mass, damping and stiffness ¨ are the hull structures vibration dismatrices respectively, X 、X 、X placement, velocity, and acceleration matrices respectively, Ft is the excitation load. Considering the fluid coupling effect, equation (4) can be rewritten as where, Fw = RTp , R is the coupling matrix, and p is the node sound pressure vector. The relationship between R and p is obtained by equation (6): where, Mw 、Kw 、C w are the fluid mass, stiffness, and damping matrices respectively, p is the first derivative of the node sound pressure vector, p¨ is the second derivative of the node sound pressure vector, and is the seawater density. The differential equation of hull-fluid coupling vibration matrix can be obtained by combining equations (5) and (6):
To calculate ship underwater radiated noise, different methods should be used for different analysis frequency bands. Therefore, dividing the frequency interval reasonably is important in calculating the ship underwater radiated noise within the full frequency. The modal number N has often been used to divide the frequency band (Yao D Y et al., 1995), which can be calculated by
M 0 R Mw
1
[ 2
A 14 ] EI
M 0 R Mw
3A hCl
+
C 0 0 Cw
X p
+
K 0
RT Kw
{ Xp } = {F0 } t
(7)
¨ X p¨
+
K 0
RT Kw
{ Xp } = {0}
(8)
The ship vibration wet mode can be obtained by solving equation (8). The study object is an offshore oil tanker with a total length of 101.60 m, as shown in Fig. 3. Based on the ship drawings, the oil tanker and fluid finite element models were established and the fluid-structure interaction (FSI) was used to define the fluid-structure coupling surface between the hull wet surface and the fluid, as shown in Fig. 4. The asymmetric method was used to calculate the ship vibration wet mode. The first 200 steps were extracted and the frequency range was 0–200 Hz. Among the obtained mode results, only the four overall modes are found, as shown in Fig. 5, and the rest are hull partial modes. The natural frequencies of the first 2 orders of the overall vertical vibration of the ship were estimated based on the ship type parameters and Todd's formula (F. H. Todd, 1948). The estimated results are shown in Table 1, the Todd's formula is:
(2)
where, is the frequency, A is the cross-sectional area of the beam structure, is the mass density, EI is the structural bending stiffness. The modal density of two-dimensional flat structure can be got by
n( ) =
¨ X p¨
Considering that the hull is undamped free vibration, equation (7) can be rewritten as
(1)
where, n ( ) is the structure modal density and f is the frequency bandwidth. The modal density is an important parameter to measure the storage capacity of subsystem vibration energy. According to the statistical energy theory, when the modal density of the substructure is larger, the modality of the substructure within the bandwidth is more dense, and the calculation result has statistical significance. The modal density of one-dimensional beam structure can be got by
1
(6)
¨ =0 Mw p¨ + C w p + Kw p + RX
2.1. Frequency band division
n( ) =
(5)
¨ + CX + KX = Ft + Fw MX
2. Middle and low frequency underwater radiated noise prediction of an oil tanker
N = n( ) f
(4)
¨ + CX + KX = Ft MX
(3)
where, h and A are the thickness and area of plate structure respectively, Cl is the structure bending wave velocity. In engineering, the low, middle, and high frequency regions are
Nv1 = 0.0167( 62
BDe3 + ) 3 VL
(9)
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Prediction of ship underwater radiated noise within full frequency
Frequency interval division
Middle and low frequency region
High frequency region
Hull vibration calculation
Acoustic and vibration coupling calculation
Hull vibration measurement
revise
bad
Realize the calculation of the ship underwater radiated noise within full frequency
Calculation accuracy evaluation
good
Hull underwater radiated noise calculation
FE-BEM
FE-IFEM
Far field criteria of ship underwater acoustic radiation
FE-AML
Comparison of calculation methods
Recommended method
Fig. 1. The flow diagram of prediction.
Fig. 3. Real ship of prediction. Fig. 2. Modal numbers of the hull structures.
where, , are ship type correction factor, for oil tanker: = 94900, = 28, V is the total mass of the ship including the surrounding seawater, V = 12933.8t, B is the ship type width, B = 14.2 m, De is the ship equivalent type deep, De = 7.5m, L is the ship vertical line length, L = 95.6 m. The Todd's formula is used to calculate the natural frequency of the first-order overall vertical vibration, and the natural frequency of the second-order vertical vibration is given by
Nv 2 = CNv1
Fig. 4. Fluid-structure interaction model and fluid-structure coupling surface (red area).
(10)
fH = (BH KH
where, C is a dimensionless coefficient, C = 2.02 . The formula for estimating the horizontal vibration mode is: 63
IH 3 HL
+ AH ) × 0.0167
(11)
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Fig. 5. The overall vibration wet mode of the ship. Table 1 The ship overall vibration mode natural frequency Hz. Order
Simulation value
Estimated value
Vibration mode
Relative error/%
1 2 3 4
1.646 1.838 3.062 4.205
1.622
First-order vertical First-order horizontal Second-order vertical Second-order horizontal
1.480
3.288
where, fH is the first horizontal vibration natural frequency, Hz; AH , BH are ship type correction factors; IH is the moment of inertia of the ship vertical axis, m4; H is the total mass of the hull and the attached seawater, t; L is the length between the hull vertical lines, m; KH is the correction coefficient of the hull profile moment of inertia. Since there is a lack of IH , the estimated value of the hull first horizontal vibration is temporarily unavailable. In engineering, the overall vertical vibration of the hull is more concerned as it has the greatest impact on the acoustic and vibration response of the ship (Weng C J, 1985). In Fig. 5, the oil tanker overall vibration mode can be divided into two major categories: vertical vibration mode and horizontal vibration mode, which appear alternately. The twisting or torsional modes usually occur in ships with large openings in the deck, such as container ships. From Table 1, the error is within 10% of the simulation values and estimated values of the first 2 vertical overall vibration natural frequency, which shows that the simulation model is credible. Through the study of the overall vibration of the hull, the basic dynamic characteristics of the ship can be more effectively grasped. The excitation frequency of the hull can be staggered from the natural frequency at the design stage, thus avoiding the occurrence of the overall resonance of the hull, which is of great significance in improving the quality and service life of the ship. Only the underwater radiated noise caused by the power plants is considered in this paper. The hull vibration response under the excitation of the main power plants was calculated. The main power
6.873
plants in the engine room include the main diesel engine, gearbox and diesel generator unit, the power plants specific parameters are shown in Table 2 and Table 3. The foot vibration accelerations of the power plants were obtained through real ship testing. Considering the test instruments, the sampling frequency is set to 16 kHz and the sampling time is set to 2 s. The measurement site is shown in Fig. 6, and the measured results are shown in Fig. 7. In engineering, the calculation of ship acoustic and vibration response is usually carried out under 1/3 octave. To study the ship underwater radiated noise characteristics of the middle and low frequency more accurately, normal spectrum density is chosen in middle and low frequency. The calculation frequency range is 20–200 Hz and the frequency interval is 2 Hz. The vibration acceleration test was performed on the local parts of the oil tanker and compared with the simulation results. The comparison results are shown in Fig. 8. The simulation overall values and Table 2 Main engine basic parameters.
64
Type
6DKM-26
Rated power Pe/kW Rated speed ne/(r/min) Number of cylinders Nc Mass/t Amount
1618 750 6 18.0 1
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Table 3 Diesel generator unit basic parameters. Type
Generator (DKBH4320/06)
Diesel engine (R6160ZC)
Rated power Pe/kW Rated speed ne/(r/min) Mass/kg Amount
160 1000 780 2
200 1000 940 2
Table 4 Comparison of simulation overall values and measured overall values in the bandwidth dB.
| t=1
At
Ft At
|
Error
Full spectrum MAPE
Engine room bulkhead Upper deck Upper deck side Poop deck Poop deck front wall Ship's cab
102.9
102.1
0.8
4.8%
79.3 102.5 82.7 73.9
77.8 96.3 83.9 70.5
1.5 6.2 1.2 3.4
14.6% 10.6% 12.0% 12.6%
86.7
88.3
1.6
16.0%
The BEM, IFEM, and AML are common numerical methods for calculating structure radiated noise in the middle and low frequency. The BEM combines classical integral equations and finite element theory. The integral equation may be regarded as an exact solution of the governing partial differential equation. The BEM attempts to use the given boundary conditions to fit boundary values into the integral equation. Once this is done, in the post-processing stage, the integral equation can be used again to calculate numerically the solution directly at any desired point in the interior of the solution domain. The infinite element method is a modification of the finite element method. The method divides the domain concerned into infinitely many sections. The structure of the acoustic IFEM is composed of two parts: the finite inner region of the envelope structure model and the semiinfinite outer region. The limited inner region is dispersed by finite elements, the semi-infinite outer region is dispersed by divergent infinite elements, and the nodes are coupled at the interface to ensure continuity in the process of outward propagation of sound pressure. The AML is a new type of finite element method. The calculation principle is to artificially set a finite thickness medium layer to absorb sound waves at the acoustic finite element boundary. The absorption layer makes sound waves decay rapidly in exponential form. Therefore, the sound wave at the boundary of the medium layer is substantially zero. There are also differences among the three methods. The BEM requires a surface mesh, but the IFEM and the AML require a volume mesh of the external sound field. Three methods are also different in acoustic boundary processing. The BEM directly takes the vibration displacement of the hull as the acoustic boundary condition, but the IFEM and the AML not only use the vibration displacement as the boundary condition, but also assign the infinite element attribute and the matching layer attribute respectively to the external sound field boundary. The BEM, IFEM, and AML were used to calculate the middle and low frequency underwater radiated noise of the oil tanker respectively. The differences in the modeling scale, computational accuracy and computational time-consuming of the three methods were explored. The calculated frequency band was 20–200 Hz with 2 Hz interval. It should be noted that the ship has a free liquid surface. In the BEM, the free liquid surface is simulated by setting anti-symmetric boundary condition, but in the IFEM and AML, the air impedance is defined at the free liquid surface. The acoustic boundary and free liquid surface processing of three methods are shown in Fig. 9. The calculated result of the oil tanker radiated sound power is shown in Fig. 10. In Fig. 10, in the range of 20–170 Hz, the radiated sound power curves obtained from the three methods agree well with each other. In the range of 170–200 Hz, the radiated sound power obtained by the FEBEM is slightly larger in amplitude than that of the FE-IFEM and FE-
measured overall values obtained by synthesizing the vibration acceleration in the bandwidth are shown in Table 4. From Fig. 8, the vibration calculation values of each measuring point have a good consistency with the measured values. The difference in amplitude is caused by factors, such as modeling error and neglect of other auxiliary mechanical equipment incentives. In Table 4, the maximum error between the simulation values and the measured values of the overall vibration acceleration level is 6.2 dB. The mean absolute percentage error (MAPE) is a measure of prediction accuracy of a forecasting method in statistics, and is defined by the formula: n
Measured value
2.3. Middle and low frequency underwater radiated noise calculation of oil tanker
Fig. 7. Frequency-domain vibration acceleration of main engine, gearbox and diesel generator unit.
100% n
Simulation value
engineering requirements and the hull vibration simulation values have good reliability and accuracy.
Fig. 6. Power plants acceleration measurement site (main diesel engine, gearbox, and diesel generator unit).
M=
Measuring point
(12)
where, At is the measured value, Ft is the simulation value. The MAPE for each one of the measuring points was calculated by using every frequency value of the spectra between 20 and 200 Hz. The full spectrum MAPEs of these measuring points are shown in Table 4. The maximum MAPE value is 16.0%, which satisfies the general
Fig. 8. Comparison of simulated and measured values for some measuring points. 65
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Anti-symmetric boundary
Vibration mapping surface
Vibration mapping surface Free liquid surface
Free liquid surface
IFEM
Fig. 9. BEM, IFEM, and AML acoustic boundary and free liquid surface processing.
AML
radiated noise. For example, the acoustic finite element boundary must be drawn as an ellipse or a sphere, and the infinite element layer thickness must satisfy 1–2 acoustic wavelengths, which will result in an increase in the number of model meshes and a reduction in computational speed. At the same time, the calculation accuracy of IFEM is related to the chosen order. Higher orders ensure high computational accuracy, but also result in poor convergence of the numerical solution. AML has no specific requirements for the boundary shape of the acoustic finite element and the thickness of the finite element layer. The acoustic calculation element numbers are much less than the IFEM, and the calculation efficiency is higher. Compared to BEM, AML needs to divide the sound field model into a volume mesh. For large models such as ships, the number of sound field grids is usually more, but BEM only needs to extract the wet surface grid of the hull structure. The BEM calculation speed is better than AML. Therefore, in engineering, the FEM-BEM method is recommended for ship underwater radiated noise calculation in the middle and low frequency. The differences in the modeling scale, computational accuracy and computational time-consuming of the three methods are shown in Table 5. The coefficient matrix of the linear equations formed by the traditional BEM is an asymmetric dense matrix, which leads to its shortcomings of high computation and high memory consumption. According to engineering experience, when the boundary element model degree of freedom N exceeds 15000, the traditional BEM will consume a lot of computer resources and a long solution time. Fast multipole BEM replaces the direct connection between the source point and the field point with the indirect connection by introducing the multipole expansion of the kernel function. The interaction between particles is replaced with the interaction between set elements. The fast multipole algorithm speeds up the multiplication of matrix and vector, and reduces the computation and memory consumption from O(N)3 to O(N), which increases the solution speed.
Fig. 10. The underwater radiated sound power of the ship.
AML. However, the calculation results of the three methods still maintain a good consistency in the trend. The overall underwater radiated sound power levels of oil tankers obtained from FE-BEM, FEIFEM, and FE-AML are 139.0 dB, 135.4 dB, and 135.8 dB respectively, and the maximum difference is 3.6 dB. Most of the sound power peak frequencies are consistent with the excitation of the power plants. Peaks at other frequencies, such as 112 Hz and 120 Hz, may be related to the vibration transmission path and the impedance characteristics of the radiated medium. The structure acoustic radiated characteristics are not only related to the excitation source, but also related to the transmission path and the radiated medium. The radiated sound pressure cloud pictures of the field points obtained by the three methods are shown in Fig. 11. In Fig. 11, at different frequencies, the radiated sound pressure levels near the excitation source are relatively large. At 22 Hz, the sound radiation of the oil tanker is mainly manifested as overall radiation, and as the frequency increases, the sound radiation gradually becomes local radiation. There are discrepancies in sound pressure distribution among the three methods, which may be due to several reasons: ① BEM calculates the sound pressure of the external sound field by surface mesh integration, while AML and IFEM calculate the sound pressure of the external sound field by volume mesh integration.② The three methods are different in boundary processing. ③ In the BEM, the free liquid surface is simulated by setting anti-symmetric boundary condition, but in the IFEM and AML, the air impedance is defined at the free liquid surface. To study the sound pressure levels of certain specific locations, three different field points are established respectively at the horizontal 100 m on the ship both sides and 100 m underwater at the center of the ship bottom. The sound pressure levels of these field points were calculated and the results are shown in Fig. 12. In Fig. 12, the radiated sound pressure spectrums are basically consistent with the ship radiated sound power spectrum, the sound pressure peak frequencies are basically the same. In the range of 20–200 Hz, the radiated sound pressure level curves obtained by the three methods agree well with each other. The sound pressure level in the ship vertical direction is greater than the horizontal direction sound pressure level at the same distance. IFEM has many limitations in the calculation of ship underwater
3. High frequency underwater radiated noise prediction for oil tanker In the high frequency region, the statistical energy method was used to calculate the ship underwater radiated noise. The SEA is a statistical method in space and frequency domain, which takes energy as a variable. Under the premise of satisfying the modal density requirement, it is of practical significance to using the SEA to predict the high frequency underwater vibration and noise of ships. The energy balance equation of a conservative acoustic-structure weakly coupled system consisting of N subsystems is (Yao D Y et al., 1995):
E ( ) = Pin ( )
(13)
where, is the frequency, is the system coupling loss factor matrix, E( ) is the subsystem energy matrix, and Pin ( ) is the subsystem input power matrix. In the high frequency, the structure radiated sound power is (Yao D Y et al., 1995):
Pr = R
2
(14)
where, R is the real part of the structure radiated sound impedance, is the hull mean square vibration velocity.
R= 66
r
M
2
(15)
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FE-BEM
FE-AML
FE-IFEM
(a) 22 Hz
(b) 48 Hz
(c) 100 Hz
Fig. 11. The underwater radiated sound pressure cloud pictures of the ship.
velocity cloud pictures are shown in Fig. 15. In Fig. 15, the hull vibration velocity near the excitation source is the largest. As the distance increases, the vibration velocity of the hull gradually decreases. From the viewpoint of the amplitude, as the frequency increases, the vibration velocity of the hull structure becomes smaller gradually. The mathematical average of the radiated sound power of the field points at three different locations are shown in Fig. 16. The radiated sound pressure levels of the three field points in the model are shown in Fig. 17, where field point 1 and field point 3 are the semi-infinite fluids on both sides of the ship and the field point 2 is the ship bottom semi-infinite fluid. In Fig. 16, the radiated sound power of the oil tanker in the range of
Fig. 12. The field points radiated sound pressure at the left, right sides and the bottom of the ship. Table 5 The differences between the three methods. Methods
Modeling scale
Computational accuracy
Time-consuming/ h
FE-BEM FE-AML FE-IFEM
small medium large
good good medium (relate to the chosen order)
3.5 8.0 11.5
where, r is the acoustic radiated loss factor, is the frequency and M is the structure mass matrix. In the high frequency band (200–8000 Hz), if the normal spectrum density is also selected to calculate ship underwater vibration and radiated noise, this would lead to a sharp increase in the number of calculation frequency points and a sharp increase in the calculation scale. Generally, there are enough frequency points between 200 and 8000 Hz in 1/3 octave to reflect the ship high frequency acoustic and vibration characteristics. The statistical energy model of the oil tankers is established, as shown in Fig. 13. The measured vibration acceleration levels of the power plants are shown in Fig. 14. The calculated frequency range is 200–8000 Hz at 1/3 octave frequency. The calculated hull vibration
Field Point 1 Field Point 3 Field Point 2 Fig. 13. The ship statistical energy model. 67
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Fig. 14. The vibration acceleration level of the power plants.
Fig. 16. Radiated sound power of oil tanker.
200–800 Hz increases slowly with frequency increasing. In the range of 800–4000 Hz, the radiated sound power starts to decrease with frequency increasing. After 4000 Hz, the radiated sound power starts to rise slowly again. In Fig. 17, the variation trend of the radiated sound pressure level curve of the three field points is basically the same as the radiated sound power curve. The field point 1 and the field point 3 are geometrically symmetrical, but the radiated sound pressure level at the field point 3 is greater than that at the field point 1 due to the fact that only the starboard diesel generator is turned on in the actual sailing condition. 4. Study on the far-field criterion of underwater acoustic radiation of ship The ship underwater radiation sound field has far field and near field, and the sound pressure has large fluctuations in the near field. For general sound sources, the radiated sound pressure decreases with distance in the far field. For a structure sound source, the sound pressure satisfies the following conditions in the far field.
P (r , , ) =
Pequ ( ,
Fig. 17. The sound pressure level of semi-infinite field point.
)
(16)
r
(r , , ) =
where, r is the distance from the field point to the equivalent sound source, and Pequ is the equivalent sound pressure amplitude, is the azimuth angle, is the elevation angle. The far-field sound pressure directivity function is
a
200 Hz
Pequ ( , ) max[Pequ ( , )/r ] r
=
Pequ ( , ) max[Pequ ( , )]
(17)
So the far-field radiation sound pressure directivity function is not related to r . The far field location can be determined when the ship
b 2000 Hz Fig. 15. The vibration cloud pictures at different frequencies of the ship. 68
c
8000 Hz
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B. Zhang et al.
Fig. 18. The sound pressure directivity of the ship.
sound radiation directivity does not change with distance. The 50 m below the center of geometry of the ship is taken as the center, four different planes of sound radiation directivity parallel to the XY plane (horizontal middle section) were established with a radius of 30 m, 50 m, 80 m, and 100 m. The BEM was used to calculate the underwater sound pressure directionality of the ship, and the results are shown in Fig. 18. The 0°, 90°, 180° and 270° respectively represent the bow, the port side, the poop, and the starboard side of the oil tanker. In Fig. 18, at all given frequencies, when the horizontal radiation radius reaches 80 m, the number of radiated sound pressure directivity side lobes no longer changes, and the directivity change laws are basically the same. In other words, after the radius of radiation reaches 80 m, the directivity of the ship radiated sound pressure no longer changes with distance. Therefore, for the oil tanker, at the underwater depth of 50 m, when the horizontal radiation radius reaches 80 m, it is already the far field of the ship underwater sound radiation.
method are reliable, and the peak frequencies of the vibration response of the hull are mostly consistent with the peak frequencies of the excitation sources. (2) The radiated sound power and sound pressure of the oil tanker obtained by the three different calculation methods are relatively consistent. Based on the analysis, FE-BEM shows a smaller modeling scale, better calculation accuracy and shorter solution time. (3) Using ship sound radiation directivity as a far-field criterion method is relatively intuitive. The far-field location of sound radiation can be determined when the sound radiation directivity no longer changes with distance. Acknowledgment This work was supported by the National Nature Science Foundation of China-P. R .China (Grant Nos. 51079118/5129148) and Defense Preresearch Project of China-P. R .China (Grant Nos. 10204010410).
4. Conclusion
References
For a certain type of oil tanker, this study firstly compares the hull vibration simulation results with the experimental results to validate the ship calculation model. Then, the FE-BEM, FE-AML, and FE-IFEM were used to calculate the middle and low frequency underwater radiated noise of the oil tanker, respectively. The differences among the three methods were explored in the modeling scale, calculation accuracy, and calculation expensiveness. The SEA was used to calculate the high frequency vibration and underwater radiated noise of the oil tanker, so that the full frequency underwater radiated noise calculation and characteristics research of the oil tanker were realized. Last, the ship sound radiation far-field criterion was studied based on sound radiation directivity. The main conclusions are summarized as follows:
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