ARTICLE IN PRESS

Ocean Engineering 36 (2009) 754–762

Contents lists available at ScienceDirect

Ocean Engineering

0029-80

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.com/locate/oceaneng

A study on propeller noise source localization in a cavitation tunnel

Cheolsoo Park a,�, Hanshin Seol a, Kwangsoo Kim a, Woojae Seong b

a Maritime and Ocean Engineering Research Institute, KORDI, Jang-dong 171, Yuseong-gu, Daejeon 305-343, Koreab Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul 151-742, Korea

a r t i c l e i n f o

Article history:

Received 16 September 2008

Accepted 17 April 2009Available online 3 May 2009

Keywords:

Noise source localization

Cavitation noise

Cavitation tunnel noise experiments

18/$ - see front matter & 2009 Elsevier Ltd. A

016/j.oceaneng.2009.04.005

esponding author. Tel.: +82 42 868 7687; fax:

ail address: parkcs@moeri.re.kr (C. Park).

a b s t r a c t

Localizing noise sources in cavitation experiments is an important research subject along with

predicting noise levels. A cavitation tunnel propeller noise localization method is presented. Propeller

noise measurement experiments were performed in the MOERI cavitation tunnel. To create cavitating

conditions, a wake-generating dummy body was devised. In addition, 10 hydrophones were put inside a

wing-shaped casing to minimize the unexpected flow inducing noise around the hydrophones. After

measuring both of the noises of the rotating propeller behind the dummy body and acoustic signals

transmitted by a virtual source, the data were processed via three objective functions based on the ideas

of matched field processing and source strength estimation to localize noises on the propeller plane. In

this paper, the measured noise analysis and the localization results are presented. Through the

experiments and the analysis, it was found that the source localization methods that have been used in

shallow water applications could be successfully adapted to the cavitation tunnel experiments.

& 2009 Elsevier Ltd. All rights reserved.

1. Introduction

As the need for high-speed and low-noise ships has increased,interest in propeller noise problems has grown. Propeller noisescome mainly from cavitation phenomena. To study cavitationnoise, facilities such as cavitation tunnels have been widely used(Blake and Sevik, 1982; Blake, 1982; Abbot et al., 1993; Friesch,1991; Boissinot et al., 1991). In cavitation tunnel test facilities,studies of cavitation and its effects are undertaken using modelpropellers by adjusting flow speeds and pressures to ensure thegeometrical and dynamic similarities between full-scale andmodel propellers.

Experimental studies of cavitation noise have been performedfor various objectives, including detecting the inception andextent of cavitation, identifying noise characteristics with respectto cavitation behaviors, and predicting cavitation noise levels(Cavitation ITTC Committee, 1978; Bark and Van Berlekom, 1978;Latorre, 1981; Koop, 1977; Thompson and Billet, 1978; Bark andJohnsson, 1981). On the contrary to the full-scale measurementswhere noise components coming from other sources such as aloud engine are included inevitably, the measurement of noiselevels generated by rotating propellers exclusively is possible inthe cavitation tunnel experiments. Since the noise levels mea-sured at the cavitation test facility are model scaled, however, thefull-scale noise levels are approximated through scaling laws

ll rights reserved.

+82 868 7683.

(Blake and Sevik, 1982; Cavitation ITTC Committee, 1987;Levkovskii, 1968; Lovik, 1981; Strasberg, 1977).

In the noise tests, it is important to understand the acousticcharacteristics of the test facility and set up the proper testprocedure for reliable measurements and analysis of the noisedata. Therefore, one of the main concerns of this cavitation noisestudy was establishing the measuring techniques or proceduresappropriate for each type of facility configuration (Blake andSevik, 1982; Blake, 1982; Cavitation ITTC Committee, 1981; TenWolde and De Bruijn, 1975; Van der Kooji and De Bruijn, 1982;Noordzji and Van der Kooji, 1981; Leggat, 1982). It has been notedthat the calibration of the facility is an important factor forobtaining proper results, especially when the acoustic environ-ment is very reverberant. Calibrating the facility means determin-ing its acoustic transfer function by using a projector and receiverset. The projector should be located at the position wherecavitation would occur. In this case, acoustic localizing thecavitation regions a priori might help improve the test quality.In addition, localizing or identifying the noise source could beused to eliminate or reduce the effect.

Acoustical holography, which is used to reconstruct the three-dimensional wave field using measurements over a two-dimen-sional surface, can be applied to find noise source positions in airand water (Maynard et al., 1985). However, there are difficulties inapplying this method to a cavitation tunnel because of thereverberant environment and the difficult placement of hydro-phones to avoid disturbing the inner flow of the tunnel. Most largecavitation tunnels in which a whole model ship can be installedutilize the beamforming technique for measuring and localizingcavitation noise using a hydrophone array set beneath the test

ARTICLE IN PRESS

C. Park et al. / Ocean Engineering 36 (2009) 754–762 755

section separated from the tunnel flow (Abbot et al., 1993; Friesch,1991). The multi-path reflections inside the test section, however,might degrade the accuracy of source localization. To overcomethe limitations of the conventional beamforming, a new signalprocessing technique called matched field processing (MFP) hasbeen investigated in the underwater acoustics community(Baggeroer et al., 1993; Tolstoy, 1993). Since MFP utilizes fullacoustic fields including multi-path components, it is adequate forshallow water applications. Therefore, the concept of the MFPcould be applied to the source localization in the cavitation tunnelthat is highly reverberant environment as well.

Our institute, MOERI, is building a large cavitation tunnel thatrequires low background noise characteristic for the noise test. Inpreparation for the new tunnel, we performed an experimentalstudy measuring and localizing propeller noises using a smallcavitation tunnel at MOERI.

In this paper, the experiments are described, and the resultsare presented. We defined three objective functions for the sourcelocalizations and compared the acoustical localization resultswith visual observations of the propeller cavitations. Section 2presents a propeller noise localization method including basicideas used in defining the objective functions. Section 3 describesthe noise experiment performed in the MOERI cavitation tunnel.Section 4 presents the results of measured data analysis andsource localizations.

2. Propeller noise localization methods

The acoustic data measured from a rotating propeller behind abody such as a ship or submarine are comprised of signals ofinterest propagated from the propeller and additional noises dueto other sources, such as unsteady flows along the body surfaceor/and tunnel walls and inherent electrical noise of measuringdevices. If we consider a specific source, the measured data d(t)can be modeled by the following equation since the propagationof the source signal s(t) through the medium can be expressed byconvolution with an impulse response h(t) in a linear timeinvariant system (Oppenheim and Schafer, 1989).

dðr; tÞ ¼ sðrs; tÞnhðr; rs; tÞ þ nðr; tÞ. (1)

In Eq. (1), � means the convolution operator, r and rs representreceiver and source positions, respectively, and n(t) is theadditional noise signal. If there are more sources, the correspond-ing terms can be simply added to the Eq. (1). Applying Fouriertransform to Eq. (1), the frequency domain expression for a singleangular frequency o becomes

Dðr;oÞ ¼ Sðrs;oÞHðr; rs;oÞ þ Nðr;oÞ. (2)

For an array of receivers, the measured noise field at all receiverpoints can be expressed by the vector D ¼ [D1, D2,y, DM]T. In thesame way, we can construct a replica field vector

_

H ¼ ½_

H1;_

H2; . . . ;_

HM�T . In shallow water applications of matched field processing,

the replica fields are usually obtained by numerical simulations.In our situations, however, real replica fields can be measureddirectly by using a virtual source at the position of

_rs that

transmits signals of waveforms known a priori. Then the scalarquantity of the replica vector at the receiver position of ri can beobtained as,

_

Hsðri;_rs;oÞ ¼ Sxyðri;

_rs;oÞ=Sxxð

_rs;oÞ, (3)

where Sxx is the autospectral density function of the virtual sourcesignal X(o), and Sxy is the cross-spectral density function betweenX(o) and its output Y(r,rs,o). Focusing on the noises generated bythe propeller, the locations of the virtual source will be confined to

the plane containing the propeller, which is called a propellerplane.

Hence, cross-correlating the measured field with the replicaleads to use of the Bartlett processor that evaluates the similaritybetween structures of two acoustic fields (Tolstoy (1993)).If the positions of the virtual source and actual source coincidewith each other, the processor will show the highest correla-tion value since the measured field vector and the replicafield vector should be similar to each other. To incorporate thebroad-banded nature of the propeller cavitation noises, anincoherent broadband processor is defined as the first objectivefunction as follows:

FBð_rsÞ ¼

1

Nf

XNf

j¼1

jPNr

i¼1Diðri;ojÞ_

H�

i ðri;_rs;ojÞj

2PNr

k¼1jDkðrk;ojÞj2PNr

k¼1j_

Hkðrk;_rs;ojÞj

2. (4)

In Eq. (4),_

H�

i means the complex conjugate of the complex value_

Hi; riand_rs represents each receiver position and the virtual source

position, respectively. In addition, Nr and Nf are the numbers ofreceiver and frequency, respectively.

As implied in Eqs. (1) and (2), the measured data at the receiverarray contain the source information, which is affected by theenvironment. Removing the environmental effects, we can extractthe source information such as source strengths and spectraldensity functions of the source signals from the data measuredfrom various receivers. The differences between the informationestimated at each receiver should be small if the real sourceposition coincides with the virtual source.

Considering the environmental effect as only a transmissionloss TL and ignoring the additional noises, a simplified sonarequation to estimate source strength SL with respect to a virtualsource position

_rs can be obtained from Eq. (2) as follows:

SLð_rs;oÞ ¼ SPLðr;oÞ � TLðr;

_rs;oÞ, (5)

where SPL represents the sound pressure level of measured data.Using the known virtual source in the tunnel, the transmissionloss can be estimated by replacing the SPL and SL in Eq. (5) withvalues of the virtual source. Then, we define the second objectivefunction to indicate whether the position of virtual source agreeswith that of noise sources as,

FSLð_rsÞ ¼ 1�

1

Nf

XNf

j¼1

1

Nr

XNr

i¼1

SLið_rs;okÞ

2�

1

Nr

XNr

i¼1

SLið_rs;okÞ

!20@

1A.

(6)

If the positions of the virtual source and actual source coincidewith each other, the processor will show the highest value sincethe source strengths estimated at different hydrophones shouldbe similar to each other.

Although Eq. (5) is a simple way to estimate the sourcestrength, additional noises are not considered in the equation.Incorporating additional noises, an optimum linear filter toestimate noise source signal from Eq. (2) can be expressed as(Papoulis, 1977)

Fðr;_rs;oÞ ¼

H

Þ

ðr;_rs;oÞSxxð

_rs;oÞ

Snnðr;oÞ þ jH

Þ

ðr;_rs;oÞj2Sxxð

_rs;oÞ

, (7)

where Snn is the autospectral density function of additionalnoises, which are measured at the same operational conditions ascorresponding propeller noise measurement tests, except that thepropeller is absent in this case. The autospectral density functionof the source signal can be estimated using that of measured dataSdd and the filter as (Bendat and Piersol, 1986)

S_

s_

sð_rs;oÞ ¼ Sddðr;oÞjFðr;

_rs;oÞj2. (8)

ARTICLE IN PRESS

Fig. 1. Schematic diagram of the MOERI cavitation tunnel.

C. Park et al. / Ocean Engineering 36 (2009) 754–762756

Then, the third objective function similar to Eq. (6) is defined by

FS_

s_

sð_rsÞ ¼ 1�

1

Nf

XNf

j¼1

1

Nr

XNr

i¼1

S_

s_

sð_rs;okÞ

2�

1

Nr

XNr

i¼1

S_

s_

sð_rs;okÞ

!20@

1A.

(9)

The estimated noise sources for the cavitating propeller can bevalidated directly via visual observations of cavitation. A compar-ison of the results using the three objective functions yields anindirect validation for the localization methods proposed in thispaper.

Fig. 2. Dummy body configuration installed in the test section of the tunnel.

3. Description of experiment

The propeller noise measurement experiment was performedin the MOERI small cavitation tunnel. The aims of the experimentwere measuring and localizing the noises generated by a modelpropeller. The cavitation tunnel has a rectangular test section,which is 0.6 m(L)�0.6 m(B)�2.6 m(H). The maximum flow speedis 12 m/s and the pressure can vary from 10 to 200 kPa.A schematic diagram of the tunnel is shown in Fig. 1.

The main objective of the cavitation tunnel is observing thecavitation patterns of model propellers. Therefore, it is veryimportant to set the flow around the propeller similarly to how itis set in a full-scale ship, and a wake screen made by layers ofvarious sized meshes is usually used for that purpose in smalltunnels like the one in this study. Since the wake screen itselfgenerates unwanted noises, it is not suitable for noise measure-ment experiments of propeller cavitation. Instead, we devised awake-generating dummy body model to put the propeller intocavitating conditions. The dummy body has a blunt shape tosimulate conventional wake fields of ships (Fig. 2).

Before the experiment, the hydro-dynamical performance ofthe dummy model was estimated via CFD analysis softwaredeveloped by the MOERI using the Reynolds averaged Navier–Stokes scheme (Kim et al., 2002). Fig. 3(a) and (b) show pressure

coefficients and velocity distribution around the body, respecti-vely. The distribution of non-dimensionalized pressure coeffi-cients of Fig. 3(a) shows high-pressure regions in front of the bluntbody and abrupt pressure drops downstream. Through thismethod, flow separations at the rear of the body were predicted,as shown in Fig. 3(b) and (c), which show axial flow velocities inthe center plane of the body and in the propeller plane,respectively. The flows accelerated around the bluntest part ofthe body and decelerated quickly after leaving that region.Eventually, the lower flow speed regions, where there wereflows with adverse directions, developed in the propeller plane.qA numerical analysis was performed based on the steady stateassumption. Considering well-developed vortex regions, however,we can expect significant unsteady flows that act as noise sourcesin the actual experiments.

We also measured the wake fields of the dummy model in theexperiment. Fig. 4 shows the iso-axial velocity curves of the wake

ARTICLE IN PRESS

Fig. 4. Iso-axial velocity curves of the measured wake.

Fig. 3. Pressure coefficients (a) and axial velocity contours at the center plane (b) and at the propeller plane (c) of the body calculated using the MOERI CFD analysis

software.

C. Park et al. / Ocean Engineering 36 (2009) 754–762 757

measured by pitottubes on the part of propeller plane occupied bythe propeller, which corresponds to the lower regions of thecalculated wake fields in Fig. 3(c). Compared to the theoreticalresults, the measured wake fields show more non-symmetricalwake distributions, which reflect the unsteady flows around thebody ignored in the numerical model. From Fig. 4, we can observethe narrow region where water flows more slowly. Cavitations aremost likely when a propeller blade passes through that region.The principal particulars of the model propeller are shown in Fig.5. The propeller used in this study is a down-scaled model withfive blades and a diameter of 250 mm.

The measuring system consisted of an array of hydrophones,signal conditioning amplifiers, and a data acquisition unit. Tenhydrophones were put inside of a wing-shaped casing tominimize the unexpected flow noise around the hydrophoneitself (Fig. 6). The hydrophone array was configured vertically atthe center of the test section approximately 1.3 m from thepropeller. The distance between adjacent hydrophones was 5 cm,which corresponds to the half wavelength of 15 kHz frequencybased on the speed of sound at 1500m/s. Since waves withwavelengths shorter than double the hydrophone spacing of auniform line array cause aliasing, only signals less than 15 kHz

will be used in data processing. In addition, we installed anadditional hydrophone upon the dummy body surface as areference.

After installing the dummy body with the propeller inside thetest section, we measured noises generated while the propellerrotating speed and flow velocity were kept constant at 20 rps andat 3 m/s, respectively. During measurements, the pressure insidethe test section was lowered gradually from 160 to 30 kPa by10 kPa steps. The corresponding cavitation numbers at the centerof the test section based on the revolution speeds of the propellerranged from 2.2 to 12.6. We also measured noises generated bythe dummy body without the propeller under the same conditionsto investigate the contributions of noises by the dummy bodyitself. As a reference we measured the background noise of theempty cavitation tunnel operated at atmospheric pressure and aflow of 3 m/s.

A B&K 8103 hydrophone/transmitter was used as a virtualsource. The input signal to the transmitter was a linear frequencymodulated (LFM) pulse train. The LFM pulse covers frequencybands of 3–15 kHz, and the time length was 1 s. Even thoughmuch lower frequencies were desired, it had to be limited to 3 kHzdue to weak transmitting sensitivity to the voltage of thehydrophone. The candidate locations of the virtual source areshown in Fig. 7. The distance between the adjacent grid points inthe surface was 1 cm. Since the array configuration of theexperiments yields azimuth angle ambiguity on horizontalplanes, we restricted the virtual source locations to the righthalf regions of the test section.

4. Noise data analysis and source localization

Fig. 8 shows the 13 octave noise levels of the dummy body and

background noise tests. The noises were measured using thereference hydrophone near the dummy body. From Fig. 8, weobserve consistent increases of noise level for the dummy bodycases compared to background noise, which might be due to theunsteady flows, such as those caused by separations around thebody. However, the dummy body is considered to generate noapparent cavitations even at the lowest pressures, since nosignificant difference in noise levels was found with pressurevariations.

The 13 octave noise levels of the dummy body with the propeller

for selected pressures are compared with the averaged noise levelof the dummy body in Fig. 9. Compared with the dummy body

ARTICLE IN PRESS

Fig. 5. Principal particulars of the model propeller.

Fig. 6. Configuration of hydrophones in a wing-shaped casing.

C. Park et al. / Ocean Engineering 36 (2009) 754–762758

(Fig. 8), we observed gradual increases of noise levels as pressuredecreased. However, significant level increases in the entirefrequency range were found only at pressures lower than 40 kPa.At higher pressure conditions, signal components of frequenciesover 1 kHz show increased noise levels relative to those of dummybody cases. Generally, vortex cavitation and small bubblesdetaching from sheet cavitation cause noise level increases inhigh frequency ranges, and large noises in low frequencies are dueto increased volumes of sheet cavitations on propeller bladesurfaces, which act like large vibrating bubbles. Therefore, it canbe postulated that fully developed cavitations are generated atpressures under 40 kPa. In addition, there seems to be highfrequency noise sources that might originate from the interactionsbetween the rotating propeller and dummy body since increasednoise levels were found at frequencies over 4 kHz even for the

160 kPa pressure condition, which is a non-cavitating conditionfor the propeller.

Fig. 10(a) and (b) show photographs of a blade taken by ahigh-speed camera at 50 and 30 kPa pressure conditions,respectively. Our hypothesis on cavitation behaviors withrespect to pressure variations can be confirmed by the figures.Up to 50 kPa (Fig. 10(a)), only a small portion of the blade wascovered with cavitating bubbles around 0.75 R of the leading edge.We also observed breaking bubbles caused by the vortex,which was detached from the body and impinging on the bladesurface of 0.7 R. At 30 kPa (Fig. 10(b)), cavitations covered halfof the blade above 0.6 R. We also observe a strong tip vortex ofthe propeller as well as the body-detached vortex. The generalcavitation behavior seems to be quite violent, since the pro-peller was not designed adaptively with respect to the wake

ARTICLE IN PRESS

C. Park et al. / Ocean Engineering 36 (2009) 754–762 759

of the dummy body. It was originally designed for a commercialship, and a normal cavitation pattern with the wake fields of theship is shown in Fig. 10(c).

Fig. 7. Grids for the ambiguity surface where the virtual source is located.

Fig. 8. One-third octave noise levels of the dummy body without the propeller for sele

3 m/s).

Fig. 9. One-third octave noise levels of the dummy body with the propeller for

The virtual source emitted linear frequency modulated wave-forms with spectral bands from 3 to 15 kHz with 1 Hz intervals.Fig. 11 shows sound pressure levels in decibels based on thereference pressure of 1mPa of the source signal located at thepropeller hub and the levels measured by the channel 5hydrophone. The source SPL reflects increasing transmittingsensitivity of the hydrophone to the pressure emitted for a unitvoltage as the frequency increased. The measured SPL showsmode interference patterns that are frequency dependent. Inaddition, the overall pressure levels of the received signal ofchannel 5 were larger than those of the source, which were mainlybecause the distance between the source and the receiver wasrelatively short and the test section is highly reverberant.

Fig. 12 shows the localization results using the objectivefunction of Eq. (4) for various pressure conditions. Each contourplot in Fig. 12, which is called an ambiguity surface, represents thenormalized power of the values calculated from the objectivefunction in decibel scale such that the maximum value equals0 dB. The dark regions in each plot indicate the possible sourcelocations. The measured noise data were digitized with samplingfrequency of 1 MHz. We prepared three sets of data at 1 Hzfrequency intervals and processed them by employing Eq. (4)using frequency components from 3 to 15 kHz. Fig. 12 presents theresults from one of the data sets processed.

From Fig. 12 two distinct noise sources are observed. The firstone is distributed on the propeller blades and the second is fromthe dummy body strut. The first identified noise source comesfrom the action of the rotating propeller. The ambiguity surfacesof 30 and 40 kPa pressure conditions show similar contourpatterns on the propeller blade and indicate a strong sourcearound 0.7 R of the upper blade. The cavitation pattern inFig. 10(b) agrees well with the propeller parts of ambiguity

cted pressures and background noise levels at atmospheric pressure (flow speed:

selected pressures and averaged body-only noise levels (flow speed: 3 m/s).

ARTICLE IN PRESS

Fig. 10. The photographs of the cavitation patterns; (a) dummy body of 50 kPa, (b) dummy body of 30 kPa, and (c) wake screen at 60 kPa.

Fig. 11. Sound pressure levels of the virtual source at the propeller hub and

measured signal using the hydrophone of channel 5.

Fig. 12. Ambiguity surfaces of 1st objective function FB, which show possible

noise sources at dark regions. The amplitude is a normalized power (decibel) of the

objective function value such that the maximum value in the plot equals 0 dB.

C. Park et al. / Ocean Engineering 36 (2009) 754–762760

surface. As we stated earlier, the cavitation was fully developed atpressures lower than 40 kPa and was expected to be the mostdominant noise source. We also observed small bubbles causedby the dummy body vortex impinging on the blades. Along withthe small portion of cavitation in the higher pressure cond-itions, the body-detached vortex explains the noise sourceslocalized in the ambiguity surfaces at 50 and 70 kPa conditions.

Even though the cavitations were weak or absent at higherpressures such as 90 and 160 kPa (Fig. 10), the propeller stillplayed an important role as a noise source. However, the sourcestrengths of the propeller at higher pressures were weakcompared with fully developed cavitations. This is supported bythe observation that the ambiguity surfaces of other data sets thatare not presented in the paper showed strong consistency atpressures of 30 and 40 kPa, and the consistency decreased as thepressure increased.

The second source of the dummy body strut existed irrespec-tive of pressure conditions. The reason for the peak of theobjective function outside the propeller disk is not obvious fromthe present experiment, and further research is needed. In ouropinion, however, interactions between the unsteady wake flowsbehind the dummy body and the rotating propeller could havecaused the noises. Another possibility is that the peak shows animage of the noise source that exists in other place than thepropeller plane due to mismatch. In MFP, the effects of mismatchmight be an interesting research field (Tolstoy, 1993; D’Spain et al.,1999). In shallow water applications, the mismatches are mainly

due to the discrepancy between the environments of measureddata and numerical replicas. In our case, the possible mismatchsources could be categorized into sources caused by testconditions and by geometries. Test conditions include pressuresand flows in measuring replica fields, which were different fromthose of noise measurements. A geometrical mismatch occurredbecause the propeller was absent when we measured replicafields on the propeller plane using the virtual source. Therefore, itis suggested that future studies be carried out to investigate thebias due to the mismatch and sensitivities of possible parameters.

Figs. 13 and 14 show the ambiguity surfaces processed by theobjective functions of Eqs. (6) and (9) for the same data set used inFig. 12, respectively. They provide localization results similar tothose of the first objective function. It is noted that the secondobjective function (Fig. 13), which includes only the transmission

ARTICLE IN PRESS

Fig. 13. Ambiguity surfaces of 2nd objective function FSL, which show possible

noise sources at dark regions. The amplitude is a normalized power (decibel) of the

objective function value such that the maximum value in the plot equals 0 dB.

Fig. 14. Ambiguity surfaces of 3rd objective function FS_

s_

s, which show possible

noise sources at dark regions. The amplitude is a normalized power (decibel) of the

objective function value such that the maximum value in the plot equals 0 dB.

C. Park et al. / Ocean Engineering 36 (2009) 754–762 761

loss term, could produce results comparable to those of the thirdfunction (Fig. 14), which incorporates additional noise compo-nents.

Comparing the three results, it is hard to tell which oneis better in terms of performance based on this limited experi-ment. However, the first objective function, which is definedusing the Bartlett processor, seems to be more robust than theothers.

The spatial resolution is an important issue in the localizationof the noise source. Although accurate spatial resolution cannot beobtained analytically in the complex environment such as acavitation tunnel, we may estimate it according to suggestion ofShang (1985) that MFP depth resolution is proportional to thewater depth divided by the highest mode number for shallowwater applications. For a perfectly reflecting rectangular ductwith the same dimension as the test section of the cavitationtunnel, the spatial resolution is estimated as around 4 cm at thehighest frequency used in the present processors. The numberof modes in the duct depends on its dimension of the cross sectionand the frequency of the noise source. The spatial resolutioncan be improved if the test is performed in a large cavitationtunnel, or noise components of frequency higher than 15 kHzare included in the processors by increasing the number ofhydrophones and decreasing the hydrophone spacing in thearray. For the present experimental set-up, the peak of theobjective functions corresponding to small scale cavitationsmight be smeared and averaged due to the limitation of theresolution scale. For a future experiment planned in a largecavitation tunnel of the MOERI, however, it is expected that thedifferent contributions of the acoustic emission of the variouscavitation phenomena can be resolved based on the methodspresented in the paper and the experimental set-up adequate forhigh spatial resolution.

5. Conclusion

Localizing noise sources in cavitation noise experiments is animportant research subject along with predicting noise levels.Through the localizing or identifying the noise source, it could beeliminated or its effect could be reduced. In addition, acousticlocalizing the cavitation regions a priori might help improve thenoise prediction test quality by an accurate calibration of a testfacility.

In this paper we proposed a propeller noise localizationmethod in a cavitation tunnel. The proposed method could be auseful tool for various applications including the acousticaldetection of cavitation inception.

We carried out noise experiment in the MOERI cavitationtunnel using a dummy body model and analyzed the measureddata. In addition, we defined three objective functions for noiselocalization based on the ideas of matched field processing andsource strength estimation and applied them to the noise dataacquired from the experiment.

The dummy body generated unsteady wake fields that causedincrease of the noise level. We also observed a gradual increase ofhigh frequency noise levels as the tunnel pressure decreased andan abrupt increase over entire frequency bands under the 40 kPapressure condition where cavitation was fully developed. Afterprocessing the noise data and replica fields measured using avirtual source, the objective functions yielded localization resultsthat agree with the visual observations.

Through the experiments and the analysis, the sourcelocalization methods that have been used in shallow waterapplications seem to be successfully adapted to the cavitationtunnel experiments.

ARTICLE IN PRESS

C. Park et al. / Ocean Engineering 36 (2009) 754–762762

Acknowledgment

This work is supported by the basic research program(PES128B) of the MOERI/KORDI.

References

Abbot, P., Celuzza, S., Etter, R., 1993. The acoustic characteristics of the NavalSurface Warfare Center’s Large Cavitation Channel (LCC). ASME Symposium onFlow Noise Modeling, Measurement and Control, New Orleans, USA.

Baggeroer, A.B., Kuperman, W.A., Mikhalevsky, P.N., 1993. An overview of matchedfield methods in ocean acoustics. IEEE Journal of Oceanic Engineering 18,401–424.

Bark, G., Van Berlekom, W., 1978. Experimental investigations of cavitation noise.In: Proceedings of 12th Symposium on Naval Hydrodynamics, Washington,D.C., USA.

Bark, G., Johnsson, C.A., 1981. Prediction of Cavitation Noise from ModelExperiments in a Large Cavitation Tunnel. Noise Sources in Ships 1: Propellers.Nordforsk, Sweden.

Bendat, J., Piersol, A., 1986. Random Data Analysis and Measurement Procedures.Wiley, NY.

Blake, W.K., 1982. Acoustic measurements in cavitation testing. In: Proceedings ofDRG Seminar on Advanced Hydrodynamic Testing Facilities, Hague, Nether-land.

Blake, W.K., Sevik, M.M., 1982. Recent developments in cavitation noise research.ASME International Symposium on Cavitation Noise, Phoenix, USA.

Boissinot, P., Fournier, P., Frechou, D., 1991. Acoustic Characterization of France’sNew Large Cavitation Tunnel. ASME Hydroacoustic Facilities, Instrumentation,and Experimental Techniques, Atlanta, USA.

Cavitation ITTC Committee, 1978. Final report and recommendations to the 15thITTC. In: Proceedings of 15th ITTC, Hague, Netherland.

Cavitation ITTC Committee, 1981. Final report and recommendations to the 16thITTC. In: Proceedings of 16th ITTC, Leningrad, Russia.

Cavitation ITTC Committee, 1987. Final report and recommendations to the 18thITTC. In: Proceedings of 18th ITTC, Kobe, Japan.

D’Spain, G.L., Murry, J.J., Hodgkiss, W.S., Booth, N.O., Schey, P.W., 1999. Mirages inshallow water matched field processing. Journal of Acoustical Society ofAmerica 105 (6), 3245–3265.

Friesch, J., 1991. HYKAT, The new cavitation test facility of Hamburg Ship ModelBasin. In: Proceedings of International Symposium on Hydro- and Aerody-namics in Marine Engineering, Varna, Bulgaria.

Kim, W.J., Kim, D.H., Van, S.H., 2002. Computational study on turbulent flowsaround modern tanker hull forms. International Journal for NumericalMethods in Fluids 38 (4), 377–406.

Koop, B., 1977. Test Procedures for Hydroacoustic Investigations in the HSVA withSome Test Results. HSVA Report No. Ac 03/77, Hamburg.

Latorre, R., 1981. Propeller tip vortex cavitation noise inception. In: Proceedings ofSNAME Propellers’81 Symposium, Virginia Beach, USA.

Leggat, L.J., 1982. Propeller noise investigation in a free-field environment. In:Proceedings of DRG Seminar on Advanced Hydrodynamic Testing Facilities,Hague, Netherland.

Levkovskii, Y.L., 1968. Modelling of cavitation noise. Soviet Physics-Acoustics 13,337–339.

Lovik, A., 1981. Scaling of Propeller Cavitation Noise. Noise Sources in Ships 1:Propellers. Nordforsk, Sweden.

Maynard, J.D., Williams, E.G., Lee, Y., 1985. Nearfield acoustic holography: I. theoryof generalized holography and the development of NAH. Journal of AcousticalSociety of America 78 (3), 1395–1413.

Noordzji, L., Van der Kooji, J., 1981. Hydro-acoustics of a cavitating screw propeller;far-field approximation. Journal of Ship Research 25, 90–94.

Oppenheim, A.V., Schafer, R.W., 1989. Discrete-Time Signal Processing. Prentice-Hall, NJ.

Papoulis, A., 1977. Signal Analysis. McGraw-Hill, NY.Shang, E.C., 1985. Matched mode localization. Journal of Acoustical Society of

America 77, 1413–1418.Strasberg, M., 1977. Propeller Cavitation Noise after 35 Years of Study. ASME Noise

and Fluids Engineering, Atlanta, USA.Ten Wolde, T., De Bruijn, A., 1975. A new method for the measurements of the

acoustical source strength of cavitating ship propellers. International Ship-building Progress 22, 385–396.

Thompson, D.E., Billet, M.L., 1978. The variation of sheet type surface cavitationnoise with cavitation number. Applied Research Laboratory, Pennsylvania StateUniversity, TM 78–203.

Tolstoy, A., 1993. Matched Field Processing for Underwater Acoustics. WorldScientific, NJ.

Van der Kooji, J., De Bruijn, A., 1982. Acoustic measurements in the NSMBdepressurized towing tank. In: Proceedings of DRG Seminar on AdvancedHydrodynamic Testing Facilities, Hague, Netherland.