Numerical Analysis of Load-noise of a Highly-skewed Propeller behind Subm arine

ZHANG Ming-yu,LIN Rui-lin,WANG Yong-sheng,FU Jian,WEI Ying-san

(College of Marine Power Engineering,Naval University of Engineering,Wuhan 430033,China)

Numerical Analysis of Load-noise of a Highly-skewed Propeller behind Subm arine

ZHANG Ming-yu,LIN Rui-lin,WANG Yong-sheng,FU Jian,WEI Ying-san

(College of Marine Power Engineering,Naval University of Engineering,Wuhan 430033,China)

This investigation combined the Computational Fluid Dynamics(CFD)with Boundary Element Method(BEM)to predict the load noise of a highly-skewed propellers behind submarine(SUBOFF)with full appendages.The credibility of CFD was validated by comparing the results derived from steady simulation of the open water propeller with experiment data.The unsteady loading(dipole sound source)on blade surface was calculated by transient simulation of the same propeller fixed after submarine and then was transferred to the sound grid.The integration of the noise source was performed over the true blade surface,which was used to predict the propeller’s low-order blade frequency noise below 1 kHz.The BEM method was used to solve the FW-H equation to get the sound pressure directivity characteristics on the 3D spherical surface enclosed the propeller as well as two planes in the surface of the propeller disc and its perpendicular surface based on theory of acoustic fan source, total sound pressure level on the downstream axial measured points were also calculated.Study shows that the sound pressure directivity on both the propeller disc and its perpendicular plane presented as‘8’,but the directivity is not unique because of the existence of rotation and skew angle of the propeller.The 3D spherical field showed that the radiant surface in the direction of the propeller disc was smaller and radiated weaker than its perpendicular plane.The results of the typical points showed that the 1st order blade frequency SPL exceeded the high-order blade frequency SPL obviously, which accorded well with fact.A good consistency had gotten after comparing with the published literature and reasonable explanation was also given to the difference.Thus,this paper introduced a new method to measure the propeller noise behind submarine in the ship effectively.

submarine;highly-skewed propeller;CFD;BEM;Acoustic Fan Source

0 Introduction

Submarine has been welcomed by navies of all ages because of its good concealment,aggressive characteristics.Submarine underwater radiated noise is one of the key factors affecting the submarine concealment in nature,which includes mechanical vibration noise,propeller noise,fluid induced noise.Propeller noise is the main source of noise,which was first foundby underwater monitor during World War II[1].Propeller cavitation noise is mainly concentrated in the high frequency band and has got improved synchronously under the medium-low speed.However,no-cavitation noise concentrated in the low frequency band performed very obviously.Currently,people began to pay attention to study this kind of noise.Both the submarine’s velocity and the propeller’s rotating speed are small,thus propeller no-cavitation noise brings greater harm.Sound field radiated by propeller mainly consists of the dipole sound noise(load noise)generated by unsteady loads[2-3]in the non-uniform flow without cavitation, so the study on no-cavitation noise of propeller fixed after submarine has a very important significance.

Zhu,Tang et al[4]had combined the unsteady lifting surface theory and acoustic methods to calculate the low-frequency discrete spectrum-line of non-cavitation noise of different propeller while effect of propellers’geometry parameters(such as propeller diameter,pitch, number of leaves,skewed,arch)to sound pressure level brought in consideration.Zhu and Wu[5]researched a propeller’s load noise characteristics based on unsteady lifting surface theory method and Goldstein theory,a brief introduction to the theoretical results and the numerical analysis method was illuminated.Seol et al[2]made a further exploration on the calculation method for calculating propeller underwater no-cavitation noise of far fields by combining the surface element method and boundary element.Analysis of unsteady propeller forces changing over time was made out and then input the forces to FW-H equation to predict the far-field sound radiation of propeller via plane element method in Ref.[3].Pantle et al[6]calculated the time-domain solution of unsteady flow field of propeller using large eddy simulation and computed its radiated noise under no-cavitation conditions through FW-H integral model.Refs. [7-8]introduced hybrid calculation method,the mutual coupling of the flow field and the sound field using the drop-coupling treatment.Sound source was the unsteady pressure resulting from the large eddy simulation,propeller noise spectrum was derived from the FW-H integral model.

This paper used large eddy simulations(LES)on the unsteady three-dimensional numerical calculations of‘submarine+propeller’through software CFX and used the boundary element method to calculate the frequency-domain load noise of a highly skewed propeller in the non-uniform flow behind the submarine based on theory for acoustic fan source,its noise distribution was analyzed and the results of the same feature points were taken out,which coincided better with the Ref.[9],the differences were also reasonably explained,studies show that Acoustic Fan Source is a new way to predict propeller noise effectively.

1 Theoretic analysis

1.1 Equation and tools

In 1969,Ffowcs Williams and Hawkings extended Curle equation to bring the impact of the moving solid boundary into consideration via generalized function,which considered prob-lems of objects moving in the fluid,such as propeller’s non-cavitation noise at work,which made the FW-H equation used more commonly[10]and laid the theoretical foundation of flow noise.

where Maris the projection of Mach number on the observer direction,S（ζ）is the acreage of moving solid.The first item on the right of equation is thickness noise,which is the noise resulting from the drain caused by blade rotation.The second term is the dipole sound source which is also known as the load noise,and is brought in by the pulse on a solid wall,the pulse can be considered only generated by fluid.Load noise plays a major role at low Mach number, this study considered the dipole sound source as the main propeller noise.The third term on the right of above equation is the quadrupole sound source generated by turbulent fluctuations in the fluid and the interaction of shear layers,which is prominent in the high Marand can be ignored when the value is low[11].

1.2 Theory for Acoustic Fan Source

There is only rotor with no stator for propeller;the expression for this acoustic field for different fan configurations is summarized as below.

Axial and tangential contributions of the radiated pressure at frequency mBΩ:

where m is the harmonic number,B is the number of rotor blades,Ω is the rotation speed,R is the distance from the observer,c0is the speed of sounds,is the Fourier series of the total force on a compact blade segment,M is the rotational Mach number,θ,φ and γ are defined in Fig.1,γ is the number of stator vanes.

Radial contribution:

Fig.1 Acoustic fan source

In the above expressions,the pressure field is computed from the loading force on a reference rotor blade.This force can be computed from the pressure fluctuations in time domain obtained from a CFD(computational fluid dynamic)computation.The computation of this force is done in a new analysis case.

The resulting loading force is applied at one point of the blade.The representation of thefan by a single fan source is a good approximation when the size of the blades is small compared to the wavelength(compact source approximation).When the size of the blade is very large and the fan cannot be considered as a compact source,the blade can be subdivided into a set of segments where each segment can be replaced by an equivalent source.

The computation of centers of gravity of segments base nodes is expressed as follows:

where xikis the k th coordinate of the i th node.The forces acting on the different segments are calculated by using the following equations:

k th component of the total force on j th segment at the i th time.Pimis the pressure at the i th time step at m th node,nodal_area_vectormkis the k th component of the nodal area vector at m th node.

2 Com puting model and numerical sim ulation

This paper used RANs method to carry out CFD calculations.Steady simulation of flow field of open water propeller was executed through solving the control equations based on SST turbulence model.Firstly,SST model combines the advantages of both k-ε model and k-ω model,k-ε model has good convergence for simulating flow in the near wall region while k-ω model has higher computational efficiency where region turbulence is fully developed[12].The three-dimensional unsteady calculations using large eddy(LES)method of the highly skewed propeller fixed behind the submarine was developed after verifying the credibility of numerical calculation,the large eddy simulation’s accuracy and resource requirements are just between DNS and RANS,the application of large-eddy simulation method has gradually expanded along with a continuous improvement of LES theory and the gradual accumulation of experience in application.We can get the propeller’s frequency-domain sound field based on theory for acoustic fan source after calculated the acoustic dipole distribution on propeller surface.

2.1 Steady state calculation and verification of open water propeller

Using software ICEM to mesh the 3D geometry of highly skewed propeller with 7 blades drew out by software Ug.The total grid number was 1 360 000,which was specifically shown in Fig.2,settings of the boundary conditions were shown in Fig.3,the number of computational domain grids was 2 100 000 while grid thickness of the first layer near the surface is 0.1 mm,the value of y+satisfied the requirement of the boundary layer turbulence required for simulation.6 working conditions at the speed 20 r/s with J=0.4～0.9 were calculated and axialthrust T and torque Q of propeller were derived through integration on the wall,which were converted into thrust coefficient,torque coefficient and efficiency as follows:

Fig.2 Geometry and structured grid of the highly skewed propeller

where D is the propeller diameter,n is the rotational speed,J is the feed ratio.

Values of thrust coefficient and torque coefficient at 20 r/s with J=0.4～0.9 were made out and curves of both the CFD values and experimental data were shown in Fig.4,the CFD values consisted with the experimental well and the error was less than 3%.

Fig.3 Computational domain and boundary conditions

Fig.4 Compared with experimental data

2.2 Unsteady three-dimensional numerical simulation of the propeller fixed behind submarine SUBOFF

The length of SUBOFF is 4.356 m,the maximum diameter is 0.508 m,podium length is 0.368 m,four empennages are arranged symmetrically in NACA0020 airfoil.The distance from the bow to propeller plane is 4.26 m.The distance on inflow direction takes a captain while twice on the out flow direction for the entire flow field computational domain whose diameter decuple the maximum boat diameter.All the mesh is hexahedral and the total number is 20 100 000.The velocity of flow was 6 kt,the outlet was set as atmospheric pressure,rotational speed of propeller was 750 r/min,steady-state time step take 0.012 s based on expression 30/(nπ),n is the rotational speed rpm.Transient calculation started on the result of steadystate.The higher sampling frequency obtained higher time resolving power of the data,pulsation amplitude may be underestimated if the sampling frequency is too low[13].This paper takes every time step from rotation time of 1°synthetically,1/(6n)=0.000 022 s.Computational domain and boundary conditions of‘boat+ propeller’were shown in Fig.5,here L is captain,D sub is the maximum diameter of the hull,and the stream lines were shown in Fig.6.

Fig.5‘Boat+propeller’boundary conditions and computational domain

3 Sound field calculation of the highly skewed propeller behind submarine

Fig.6 Streamline

3.1 Data transfer

Extracting the propeller surface pressure after the above three-dimensional unsteady calculation was convergent and mapped it onto the sound grid through distance-weighted method. This paper imported the pressure datum of 360 time steps,namely 1 circuit of propeller.λ=c/ f,f≤1 kHz,the wavelength is at least 1.5 m so that there were enough units to describe the sound field within each wavelength even though the size of acoustic grid cell was a little larger.Acoustic Fan Source just takes one blade to calculate sound field and then describe the work of the propeller blades by defining the number of blades and rotational speed.The sound pressure information of a skewed propeller blades to a corresponding sound field grid was transferred by nodes scale 4:1,grids and pressure distribution were shown in Figs.7 and 8.

Fig.7 Fluid mesh

sound grid

Fig.8 Pressure extracted from CFD mapped pressure

3.2 Acoustic Fan Source settings and number verification of dipole segments

Dividing the blade into segments after defining the rotating coordinate, each block will be treated as an equivalent dipole sound source.The results of 13 and 34 segments under 1BPF (Blade Passing Frequency)showed that the sound directivity overlapped substantially on both propeller disk and its vertical surface,which verified theindependence of the number of dipole segments.The segments and corresponding results of sound directivity were shown in Fig.9.Rotational speed of propeller is 12.5 r/s,the number of blades is 7,the time domain information is transformed into the frequency domain though Fast Fourier Transform.

Fig.9 Segments and results

4 Sound field analyses

Two panel sound fields,which were on propeller disc and the axial longitudinal section of the highly skewed propeller,and a spherical sound field were established respectively,all of whose center were the geometric center of the propeller and all their diameters were the 10 times of the propeller diameter.This paper analyzed all the sound fields in detail based on fact and corresponding theory.Results of the same feature point with Ref.[9]were calculated and consisted well with Ref.[9].

4.1 Sound directivity analysis

Sound directivity is an important item on analyzing the characterization of sound field, this paper analyzed two panel sound field respectively on propeller disc and the axial longitudinal section of the highly skewed propeller.The sound pressure level(SPL)in blade passing frequency and its harmonics were shown in Figs.10 and 11.As can be seen,both the surface sound fields can be observed two strong and weak radiation directions in the shape of‘8’, which was determined by the dipole sound source,but the directivity is not unique because of the existence of rotation and skew angle of propeller.We can also see that the SPL is slightly lower on propeller disc than that of the axial longitudinal section.

Fig.11 Axial longitudinal section of the sound field directivity

4.2 Spherical field analysis

Analysis to the sound field distribution of the spherical field at different frequencies was shown in Fig.12.The SPL is the highest in axial direction of the propeller and gradually decreases along with the increase of axial angle.Sound source area perpendicular to the propagation direction is smaller in the radial direction,which is contrary to the axial direction.So the propeller load noise radiates strongly in the axial direction and weakly on the radial direction,which is consistent with the mechanism of the propeller load noise.

Fig.12 SPL distributions on spherical field

4.3 Analysis of feature points

Three feature points were arranged on a circle,whose distance to the geometric center of the propeller is 10R(R is the radius of the propeller).Their specific position and spectrogram were shown in Fig.13,the point 3 is in the axial direction of propeller,which is the same with the feature point of Ref.[9]. The sound spectrum of feature points also incarnated that SPL is the highest in axial direction of the propeller.

Fig.13 Feature points’arrangement and sound pressure spectrum

Tab.1 Results contrast of feature point 3

Fig.14 Results of feature point3

5 Conclusions

The credibility of CFD was validated firstly by comparing the results derived from steady simulation of the open water propeller with experiment data.The unsteady loading(dipole source)on blade surface was calculated by transient simulation of the same propeller fixed after submarine and then was transferred to the acoustical mesh nodes.The BEM method based on Acoustic Fan Source theory was used to solve the FW-H equation to get the sound directivity characteristics on three sound fields.Studies show that:

(1)Both the surface sound fields can be observed by two strong and two weak radiation directions in the shape of 8,which are determined by the dipole sound source,but the directivity is not unique because of the existence of rotation and skew angle of propeller.We can alsosee that the SPL is slightly lower on propeller disc than that of the axial longitudinal section.

(2)Sound source area perpendicular to the propagation direction is smaller in the radial direction,which is contrary to the axial direction,so the propeller load noise radiates strongly in the axial direction and weakly in radial direction,which is consistent with the mechanism of the propeller load noise.

(3)The results of the feature points showed that the SPL value at 1st order blade frequency exceeded SPL value at high-order blade frequency obviously,The SPL value of feature point 3 below 1 kHz is 99.7 dB under J=0.88,rotational speed=12.5 r/s,which consisted well with Ref.[9].

Studies show that Acoustic Fan Source is a new way of predicting propeller noise effectively.

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艇后大側(cè)斜螺旋槳負載噪聲數(shù)值分析

張明宇，林瑞霖，王永生，付建，魏應三

（海軍工程大學動力工程學院，武漢430033）

為研究艇后非均勻流場中大側(cè)斜螺旋槳無空泡負載噪聲的分布規(guī)律，文章采用“CFD+BEM”法，以SUBOFF潛艇后某大側(cè)斜槳為研究對象，首先穩(wěn)態(tài)計算均勻進流下螺旋槳敞水特性，模擬系數(shù)值與實驗誤差在3%以內(nèi)，驗證了CFD數(shù)值計算的可信性。然后采用大渦（LES）模擬，對“艇+槳”進行三維非定常數(shù)值模擬，計算得到槳表面聲偶極子數(shù)據(jù)后，通過距離加權(quán)平均法映射到聲網(wǎng)格節(jié)點上，將噪聲源直接分布在槳葉表面上進行積分來預報螺旋槳的低頻線譜噪聲。采用邊界元法基于扇聲源理論通過FW-H聲類比方程分別在1 kHz以內(nèi)對槳盤面、軸向縱剖面及10倍槳半徑球場的噪聲進行頻域求解。研究表明：槳盤面和軸向縱剖面上聲指向均呈8字形，但受螺旋槳自身旋轉(zhuǎn)及大側(cè)斜的存在，指向性不唯一；球場聲場顯示，軸向聲輻射面較大，聲輻射強，徑向輻射面小且輻射較弱；特征點的計算結(jié)果顯示，高階葉頻聲壓級明顯比一階葉頻低，這與物理現(xiàn)象相符，將特征點處結(jié)果與已發(fā)表文獻進行對比，吻合性良好，并對存在的差異作出了合理的物理解釋。該文為螺旋槳噪聲預報介紹了一種可行的新方法。

潛艇；大側(cè)斜螺旋槳；計算流體力學；邊界元法；扇聲源理論

U664.33

A

國家自然科學基金資助項目（51009144）

張明宇（1989-），男，海軍工程大學動力工程學院博士研究生，E-mail：yijianmingyu@163.com；林瑞霖（1955-），男，博士，海軍工程大學動力工程學院教授，博士生導師；王永生（1955-），男，海軍工程大學動力工程學院教授，博士生導師；付建（1985-），男，海軍工程大學動力工程學院博士；魏應三（1984-），男，海軍工程大學動力工程學院講師。

U664.33

A

10.3969/j.issn.1007-7294.2016.09.010

1007-7294（2016）09-1190-11

Received date：2016-01-17

Foundation item:Supported by National Nature Science Foundation of China(51009144)

Biography：Zhang Ming-yu(1989-),male,Ph.D.candidate,E-mail:yijianmingyu@163.com; LIN Rui-lin(1957-),male,professor/tutor.