LEE Jeung-Hoon, JUNG Jae-Kwon, LEE Kyung-Jun, HAN Jae-Moon, PARK Hyung-Gil, SEO Jong-Soo

Samsung Ship Model Basin (SSMB), Marine Research Institute, Samsung Heavy Industries, Science Town, Daejeon 305-380, Korea, E-mail: jhope.lee@samsung.com

(Received May 22, 2012, Revised August 10, 2012)

EXPERIMENTAL ESTIMATION OF A SCALING EXPONENT FOR TIP VORTEX CAVITATION VIA ITS INCEPTION TEST IN FULL- AND MODEL-SHIP*

LEE Jeung-Hoon, JUNG Jae-Kwon, LEE Kyung-Jun, HAN Jae-Moon, PARK Hyung-Gil, SEO Jong-Soo

Samsung Ship Model Basin (SSMB), Marine Research Institute, Samsung Heavy Industries, Science Town, Daejeon 305-380, Korea, E-mail: jhope.lee@samsung.com

(Received May 22, 2012, Revised August 10, 2012)

Tip vortex cavitation noise of marine propeller became primary concerns to reduce hazardous environmental impacts from commercial ship or to keep the underwater surveillance of naval ships. The investigations of the tip vortex and its induced noise are normally conducted through the model test in a water cavitation tunnel. However the Reynolds number of model-test is much smaller than that of the full-scale, which subsequently results in the difference of tip vortex cavitation inception. Hence, the scaling law between model- and full-scales needs to be identified prior to the prediction and assessment of propeller noise in full scale. From previous researches, it is generally known that the incipient caivtation number of tip vortex can be represented as a power of the Reynolds number. However, the power exponent for scaling, which is the main focus of this research, has not been clearly studied yet. This paper deals with the estimation of scaling exponent based on tip vortex cavitation inception test in both full- and model-scale ships. Acoustical measurements as well as several kind of signal processing technique for an inception criterion suggest the scaling exponent as 0.30. The scaling value proposed in this study shows slight difference to the one of most recent research. Besides, extrapolation of model-ship noise measurement using the proposed one predicts the full-scale noise measurement with an acceptable discrepancy.

tip vortex cavitation, underwater radiated noise, scaling exponent

Introduction

Among the main contributions to underwater radiated noise of marine transportations, the most prevalent source is the noise from the cavitation of propellers. Cavitation is a vaporization phenomenon caused by a sudden decrease in static pressure of a flow. When the pressure in a fluid is reduced below a certain value, the fluid begins to evaporate over pre-existing nuclei, thus forcing them to grow. Flowing into the downstream, the bubbles collapse in the high-pressure region by accompanying an emission of impactlike sound. Once the cavitation occurs, its subsequent noise becomes to dominate over the other noise sources from the main engine, hull structure, etc..

The cavitation is classified by its features such as sheet cavitation, tip vortex cavitation, and so on. Eachtype has its own inherent acoustic characteristics. The tip vortex cavitation, typically bursting in the trailing vortex, is regarded as the main source of cavitation noise dwelling in a broad-banded frequency ranges[1,2]. Hence the noise induced by tip vortex cavitation and its prediction have become of interest to the marine engineers and ship designers.

Because of complicated flow- and noise- field making a theoretical approach difficult, tip vortex cavitation noise in full scale strongly depends on extrapolation of the model-scale measurement in a cavitation tunnel. However the model test at the Reynolds number (Re) much lower than that for the corresponding full-scale causes the difference in the inception of tip vortex. In other words, the tip vortex cavitation in full-ship case appears at a higher cavitation number (or lower ship speed) than that of the model ship. Undoubtedly scaling law for tip vortex cavitation needs to be clarified prior to the estimation of noisecharacteristics in full-scale.

Based on the analysis of hydrofoil, McCormick[3]firstly proposed that the incipient cavitation number of tip vortex σican be represented as a power function of the Reynolds number with the scaling exponent 0.4, i.e., σ～Rekwith k=0.4. But the relationship is

i valid only for Re＜105. In other words, it is inappropriate to employ the exponent 0.4 for a high Reynolds number application, since the Reynolds number in full scale is usually larger than O(107). Jessup et al.[4]obtained an intolerable result when the exponent 0.4 was applied to model test for the prediction of tip vortex behavior in full scale. Almost no scaling, in fact, was necessary to correlate with the full-scale data. This was the same case with Oshima[5], wherein the proposed exponent was about 0.15. Moreover, Amromin[6]suggested two-range scaling, 0.4 for Re＜6×106and 0.24 for Re>6×106. Shen et al.[7], in their recent research for the scaling of tip vortex cavtation, states that the exponent is not a constant but a variable with respect to the Reynolds number.

As can be seen in the previous researches, the determination of the scaling exponent is not only very active, but also arguing issue in the field of underwater radiated noise study. It should be emphasized that the cases using the full- and corresponding model-scale measurement data are rarely found in the world. Needless to say, more experimental data including full-scale cases are essential for a reliable estimation.

This motivates us to estimate the scaling exponent via cavitation inception tests in both model- and full-scale ship, which will be detailed in Section 1. Several kinds of signal processing techniques for an acoustical inception criterion will be illustrated as well. Section 2 covers the prediction of full-scale noise by using the scaling exponent proposed in this study. Its comparison to the actual measurements will also be discussed. Finally, this paper is closed with conclusions in Section 3.

Table 1 Specifications of test vessel (crude oil tanker)

1. Tip vortex cavitation inception test of the fulland model- ship

Table 1 summarizes the specification of the test vessel for the experimental determination of scaling exponent k. The examined ship is a commercial crude oil tanker (the Suezmax class), having a six-cylinder two-stroke diesel engine and a four-bladed propeller as well. The comparisons between model- and fullscale data are difficult because model tests are typically based on visual inspection and full-scale ones and are more often based on acoustic noise signal. This might cause a variation of a few knots in the inception speed, resulting in an incorrect estimation for the exponent. Indeed, when the cavity is observed visually there might be an ambiguity between the experimenters. To avoid such confusion, the authors decided to adopt acoustical criteria only.

1.1 Model ship test

The cavitation inception test for the model ship was carried out in the water tunnel of the Samsung Ship Model Basin (SSMB). The general arrangement and principal particulars of the tunnel are presented in Fig.1 and Table 2, respectively. The test section of 3.0 m width, 1.4 m height and 12.0 m length is able to accommodate the complete model, which was manufactured of wood to a scale ratio of 1:36.36. Inside the model ship, a water tight dynamometer was installed for the measurement of thrust, torque and rate of revolution of the model propeller. Wooden plates were placed between the tunnel wall and the model ship at the height corresponding to the scaled design draught to suppress free water surface. Figure 2 shows the complete model ship installed in the water tunnel.

The miniature hydrophone (Model: B&K 8103) was also flush-mounted on the hull surface just above the propeller. The signals from the hydrophone were passed through the signal conditioner (Model: B&K 2690), and logged into the PC-based measurement system with a sampling frequency of 256 kHz. Extrapolation of model data to full-scale, which will be treated in later section, caused the lack of data to compare with actual full-scale measurement due to the frequency scaling. Thus the sampling frequency in the model-scale test needs to be higher than that in full scale to moderate the frequency scaling.

The operational profile of the ship was beforehand determined from the powering performance tests in the towing tank of SSMB. Then the propeller is tested at a prescribed set of two non-dimensional numbers: the thrust coefficient Ktand the cavitation number σn,

Fig.1 General arrangement of water cavitation tunnel in SSMB. Model test was conducted at No. 2 test section

Table 2 Principal particulars of test section

Fig.2 Complete model ship mounted in the water cavitation tunnel

where T denotes the thrust force of propeller,ρ the water density, n the rate of revolution of propeller (rps),D the diameter of propeller, pathe atomspheric pressure,g the gravitational acceleration, hthe vertical distance between the water surface and the center of propeller, and pvthe vapor pressure depending on temperature. To reach the propulsion point, the flow speed in the tunnel was firstly controlled, high enough to acquire sufficiently high Reynolds number. Then the propeller rps was adjusted to the value giving the desired thrust coefficient on the basis of thrust identity[4,8]. After achieving the thrust identity, the tunnel was depressurized to meet the prescribed cavitation number.

The test condition of ship speed in this study ranges from 12 kts to 19 kts. To obtain correspondent speed condition, the water flow speed and the pressure were varied between 4.90 m/s and 4.97 m/s, 0.40× 105Pa and 1.18×105Pa, respectively, whilst keeping the propeller rps as 28.3 (1 700 RPM). Model test conditions for the operation profile are summarized in Table 3. In addition, the Reynolds number for each test condition shown in the last column was calculated by the following,

where ν designates the kinetic viscosity of the water, and c the chord length of the propeller at 0.9 propeller radius. Further, Vrdenotes the resultant water velocity at that radius, which is defined by the triangular relationship between axial- and rotational- velocities

Table 3 Operational profile and conditions of model test

The axial inflow velocity componentAV can be estimated by using the propeller open water characteristics and the wake distribution in the propeller plane.

One of the important factors in the cavitation inception tests and accordingly in the noise measurements is the quantity of air (or nuclei) content in the water[3,9]. For a correct extrapolation of the model test data to the full-scale, the air content of the water needs to be fully saturated to correspond with that of seawater. As a normal practice in SSMB, the air content of the water was kept at 50% through a deaeration process.

Fig.3 Power spectral densities for noise measurement in the model-scale ship, Parameters of spectrum estimation: Hanning window, 1 000 times ensemble average, 75% overlapping, one-third octave-bandwidth frequency resolution

Figure3 represents measurements of the acoustic signal for each speed conditions, where the power spectral densities was estimated by applying the Hanning window and ensemble average of 1 000 times with 75% overlapping, and observed with the one-third octave-bandwidth frequency resolution[10]. For a validation of measured signal, background noise at the 12 kts condition shown as thin black line was measured under the configuration of dummy hub, i.e., w/o propeller blades. Shaft rotation as well as water flow in the tunnel seems to affect the noise in low frequency range below 100 Hz, which is out of interest. Except the frequency below 100 Hz, measurements with blades is approximately 10 dB larger than the background noise. Hence the model-scale noise measurement in this study can be considered as valid one.

Fig.4 Overall sound pressure level for model-scale noise measurement. Summation bandwidth: 1 kHz-100 kHz

Increase in sound pressure level is visible with ship speed condition at a first glance. In more detail, blade frequency component ranging from 100 Hz to 500 Hz began to increase from 16 kts condition. The broad-band noise above 1 kHz was also enlarged withship speed, which could be presumably suspected by the growth of tip vortex cavitation. However, the typical spectral analysis in the above did not provide a clear evidence of cavitation inception. In order to examine the measured signal further, following signal analysis of overall level, Detection of Envelope Modulation On Noise (DEMON)[11]and Short Time Fouier Transform (STFT)[10,12]were carried out.

Fig .5 DEMON spectrum of model-scale measurement. Unitof contour level is the modulus of DEMON spectrum

Figure 4 depicts the variation of overall sound pressure level along with the ship speed condition, the summation bandwidth of which was taken from 1 kHz to 100 kHz. One can easily observe the 3dB increment starting from 15 kts speed condition. The instant when the noise level begins to increase is normally accepted as a cavitation inception speed. Thus sufficient raise in noise level can be regarded as an indication of cavitation inception. Furthermore, DEMON analysis shown in Fig.5 would give an interesting investigation. White tick marker on the top of each DEMON spectra denotes the frequencies of propeller rps and its harmonics. Especially, every 4th ticks were spotted with thick and long marker to represent blade frequency components. At 14 kts condition (see Fig.5(a)), no diagnostic frequency component is shown in the DEMON spectra, which implies no cavity on the propeller blade. In Fig.5(b), we can see the emergence of shaft frequency and its harmonic components at 14.5 kts condition, representing a cavitation inception at one blade only.This can be attributed to the manufacturing tolerance of model propeller. Generally tip vortex cavitation, especially in the model propeller, does not occur simultaneously at all blades due to geometrical tolerance, instead one or two blades among the other reveal an early tip vortex. Normally, for that reason, the presence of shaft frequency modulation is not treated as an inception. In our case, it seems that one blade among the four begins to exhibit cavitation. The timefrequency analysis using STFT verifies such a phenomenon. For 14.5 kts condition, the upper plot of Fig.6(a) represents measured time signal for a period of one shaft revolution, and the lower does the corresponding STFT analysis. Only one event of cavitation ranging about several tens of kilo-hertz can be detected during a revolution. This explains why the shaft frequency modulation is rendered the DEMON spectra of 14.5 kts speed condition in Fig.5(b).

Fig .6 Time signal and time-frequency analysis for the one period of propeller revolution, model-scale measurement. Unit of contour level is in dB with the dB reference value of 1 μPa

Fig.7 A photo of tip vortex cavitation inception taken under 15 kts condition

Fig.8 Hydrophone and pressure transducer flus h-mounted on hull surface using bottom plug

Table 4 Test condition of full-scale noise measurements

Figure 6(b) shows the STFT analysisresult for the 15 kts condition exhibiting three distinct cavitation events. Even though caviation at one blade is missed, the appearance of blade frequency becomes clearer than in the 14.5 kts case as shown in DEMON spectra of Fig.5(c). For the 16 kts condition, where the cavitation is further developed, strong existence of the blade frequency can be perceived as shown in Fig.5(d). The above analysis for the measured noise data is enough to decide the 15 kts condition as cavitation inception in the model scale. For reference, a photo of tip vortex cavitation taken under the 15 kts condition is shown in Fig.7.

1.2 Full-ship test

The sea trialfor the full-ship test was performed at aneven draft of 16.0 m. Typical full-scale measurements for underwater radiated noise were usually conducted using buoys at which hydrophones are suspended at several depths. However, in this study, the miniature hydrophone (model: B&K 8103) was placed on the identical position with the model-test case by employing a bottom plug system. Sampling frequency for full-scale measurement was set as 51.2 kHz, a quarter of the one in model-scale. Next to the hydrophone, pressure transducer (model: the Kulite XTL-190) was also installed to read the DC (0 Hz) value, i.e., static pressure, and accordingly to calculate the cavitation numbernσ in Eq.(1). Figure 8 represents the hydrophone and the pressure transducer, flush-mounted on the hull surface above the propeller. Also the figure shows a bottom plug system for the mounting of hydrophone. While the ship was in the condition of straight sea-going at the Beaufort scale 2[13], the speed was varied from 7.8 kts to 16.6 kts by increasing the propeller rps. The ship speed, corresponding propeller rps, cavitation- and Reynolds number are summarized in Table 4.

Fig.9 Power spectral densities for noise measurement in the full-scale ship. Parameters of spectrum estimation: Hanning window, 95 times ensemble average, 75% overlapping, one-third octave-bandwidth frequency resolution

Fig.10 Overall sound pressure level for full-scale noise measurement. Summation bandwidth: 20 Hz-20 kHz

Figures 9 and 10 represent power spectral densities and the overall sound pressure level along the ship speed, respectively. It is still ambiguous to resolve the cavitation inception based on power spectrum data. On the other hand, overall level, the summation bandwidth of which was between 20 Hz and 20 kHz, provides a clue for an inception by noting a sudden noise increase (approximately 3 dB) starting at 8.8 kts condition. Consecutive DEMON analysis shown in Fig.11 undoubtedly supports such observations.

Fig.11 DEMON spectrum of full-scale measurement. Unit of contour level is the modulus of DEMON spectrum

Before proceeding, the 6th component of propeller rps, resulting from the gas combustion in the cylinder of the main engine, is noticeable in DEMON spectra of 7.8 kts-9.8 kts condition as shown in Figs.11(a)-11(c). Because of two cycle type engine regime, there is only one time of gas combustion per each cylinder during a period of one propeller revolution. Eventually the combustion events during a propeller revolution occurred for six times, which corresponded to the number of cylinders in the main engine. Once again, the STFT analysis can be necessarily applied to visualize these events. Figure 12(a) represents measured time signal and STFT analysis for 7.8 kts condition, exhibiting six impact events induced by gas combustion.

Fig.12 Time signal and time-frequency analysis for the one period of propeller revolution, full-scale measurement. Unit of contour level is in dB with the dB reference value of 1 μPa

The Existence of blade frequencies (the 4× com-ponent and its harmonics), the key proof of cavitation inception, can be seen in Fig.11(b) representing the DEMON spectra of 8.8 kts condition. In the inception stage, the noise contribution of main engine is still dominant compared to the one of cavitation, as shown in Fig.12(b). Hence STFT-based cavitation detection can be disturbed when the other noise sources together with the existing cavitation. At a higher speed condition of 9.8 kts shown in Fig.11(c), the cavitation seems to develop far beyond by noting that the 4× component is superior to the 6× one representing gas combustion. Finally, only the blade frequency components are observed at the highest speed condition 16.6 kts in Figure 11(d), where the cavitation has developed sufficiently. For reference, the STFT analysis for the 16.6 kts condition is also shown in Fig.12(c). The illustration represents both four distinct impact events during a propeller revolution. And the pressure magnitude of the cavitation is much larger than that of the gas combustion. Based on the above analysis, we can conclude the condition of 8.8 kts as the cavitation inception in the full-scale ship.

Table 5 Summary of cavitation inception test

2. Estimation of scaling exponent and its application to the full-scale noise prediction

So far we have discussed about cavitation inception test for the full- and model- ship, the summarization of which is given in Table 5. For an estimation of scaling exponent based on the test data, Reynolds number dependence of tip vortex cavitation inception, i.e., σi～Rek, can be rewritten as follows

where the subscripts s and m denote full- and model-ships, respectively. Then the scaling exponent can be expressed as Eq.(5) given below

The exponentk =0.3 can be obtained with the above. Definitely the proposed one can have an error inits estimate, especially originated from Reynolds number calculation. Both the viscosity ν and axial velocity component in the propeller plane VAinfluence to a degree in the estimation of Reynolds number. For example, when those two parameters of ν and VAare independently varied from -20% to+20%, the resultant scaling exponent ranges between 0.28 and 0.31, i.e., 3% estimation error. In spite of its variety, it should be emphasized that the proposed value is considerably smaller than k=0.4 used widely today. As mentioned in Introduction, there have been many statements about unsatisfactory results of scaling with the exponent 0.4 for marine propellers in papers published by Jessup et al.[4], Shen et al.[7], and others. However, due to the shortage of the other cases, it is not certain to use generally the value of k as 0.30, which was found in the present study.

The most recent research[7]states that the exponent is not a constant, but a variable with respect to the Reynolds number. Using a logarithmic lawto d escribethe velocity profile in the boundary layer over a large range of Reynolds number which is just in the case of this study, the exponent could be derived to a dependent on the values of the model- and full- scale Reynolds numbers as follows

This suggests k=0.32, very closeto the proposed onein this study. Such a reasonable agreement with the available theory encouraged us to predict thefullscale noise using the model-scale measurements.

To expandthe model-scale noise spectra into the full-ship, normally used noise-scaling formula was recommended by the International Towing Tank Conference (ITTC)[14],

In the above, the first accounts for the scalingof frequency, and the second the power spectral density of the sound pressure level.fdenotes the frequency,Gthe power spectral density and r the distance between the hydrophone and the cavitationcenter. As is shown in frequency scaling formula, extrapolated frequency using the model-scale data is shifted to the lower one, and causes a lack of data to compare with actual full-scale measurement. Thus the sampling frequency for the model-scale noise measurement needs to be much higher than that of the full scale.

Further, due to the cavitation number term, the frequency scaling in Eq.(7) does not correctly predict the blades tonals in low frequency range, mainly occuring from sheet types cavitation. For those well-developed cavitation, it is reasonable to assume a geometrical similarity in model- and full-scales at equal speed condition (or equal cavitation number), yielding an elimination of the cavitation number term in the ITTCformula. Equation (7) obviously holds for high frequency range, where the tip vortex cavitation noise dominates. Hence, the full-scale noise prediction in this study will concern the high frequency above 100 Hz.

Fig.13Full-scale noise prediction for 8.8 kts conditionand comparison with actual measurements. Powerspectral density representation

Full-scale noise data at the inception speed conditionof 8.8 kts is adopted from Fig.9 again for convenience, and represented as circle symbol in Fig.13. Fora prediction, it was previously mentioned that the corresponding speed condition in model scale should be made at a much higher than target one in the full scale due to the Reynolds number dependency of tip vortex cavitation. If the scaling exponent is assumed tobe0.4, the corresponding cavitation number can be calculated as 2.45 from Eq.(4). Accordingly, the model-scale measurement under the speed condition of 18 kts is required for a prediction. The calculation with Eq.(7) is shown as square symbol in Fig.13, exhibiting a significant over-estimating error with the actual measurement. The 18 kts condition in modelscale actually reveals a developed cavitation as shown in Fig.14. Thus such a developed cavitation far beyond the inception stage is considered to have effects on the over-estimation of full-scale measurement.

Fig.14 A photo of tip vortex cavitation inception taken under 18 kts condition in model-scale ship

On the other hand, when the prediction isbased on scaling exponent 0.30, model-scale measurement under 15 kts speed condition would be needed. Predictionwith k=0.3 is shown as triangle symbol in Fig.13. Although qualitative behavior between the prediction and the measurement agrees well, it can be observed that the full-scale measurement is mainly under-estimated by 6 dB in average. Herein one needs to remind that the full-scale measurement under the cavitation inception condition includes not only the contribution of tip vortex cavitation but also the one of machineries including main engine which cannot be described by a model test. Under-estimation, therefore, is inevitable near the cavitation inception since the effect of machineries cannot be neglected. However such contribution will be decreased with the increase of ship speed beyond the cavitation inception.

Fig.15Full-scale noise prediction for 9.8 kts conditionand comparison with actual measurements, powerspectral density representation

To see this, it is essential to predict noisespectra under ahigher speed condition of 9.8 kts in full-scale, where the cavitation is under developmentand the noise induced by the cavitation is dominant. In this case, the prediction shown in Fig.15 was based on the model-scale measurement at the 19 kts speed condition. Even though the pre diction still under-estimatesthe measurements, the overall discrepancy is decreased to 4 dB with an acceptable error bound. If the scaling exponent of 0.4 was applied for a prediction, but which cannot be done by the current set of model test data, a significant over-estimation would be obtained. Hence, based on the above illustrations, the proposed exponent for the scaling of tip vortex cavitation can be considered as a valid one.

3. Concluding remarks

The aim of this research is to determine the exponent for scaling of tip vortex cavitation prior to a prediction of under-water radiated noise of a marine propeller. To this end, tip vortex cavitation inception tests were performed in model- and full-scale ships. An acoustical measurement together with DEMON and STFT analysis was successfully employed for a criterion of cavitation inception. The estimated scaling exponent k is found to be around 0.30, which is noticeably smaller than =0.4k used widely today. It is remarkable that the exponent in this research is very close to the one of theoretical work by Shen et. al.[7]Besides, the application of =0.3k to the prediction of full-scale noise shows an acceptable correlation with the actual measurement.

Although it is not confirmative to generalize the present result, the approach taken in this study would give a guideline for the determination of scaling exponent. Nevertheless, more experimental data in both model- and full- scales are necessary to fully validate the proposed value.

[1] ROSS D. Mechanics of underwater noise[M]. New York, USA: Pergamon Press, 1976.

[2] CARLTON J. Marine propellers and propulsion[M]. 2nd Edition, USA, Massachusetts: Butterworth- Heinemann, 2007.

[3] MCCORMICK B. W. On cavitation produced by a vortex trailing from a lifting surfaces[J]. Journal of Basic Engineering, 1962, 84(3): 369-379.

[4] JESSUP S. D., REMMERS K. D. and BERBERICH W. G. Comparative cavitation performance evaluation of a naval surface ship propeller[C]. Cavitation Inception, ASME FED. 1993, 177: 51-63.

[5]OSHIMA A. A study on correlation of vortex cavitation noise of propeller measured in model experiments and full scale[J]. Journal of the Society of Naval Architects of Japan, 1990, 168: 89-96.

[6] AMROMIN E. Two range scaling for tip vortex cavitation inception[J]. Ocean Engineering, 2006, 33(3-4): 530-534.

[7]SHEN Y. T., GOWING S. and JESSUP S. Tip vortex cavitation inception scaling forhigh Reynolds number applications[J]. Journal of Fluids Engineering, 2009, 131(7): 071301.

[8] FRIESCH J., JOHANNSEN C. and PAYER H. G. Correlation studies on propeller cavitation making use of a large cavitation tunnel[C]. SNAME Annual Meeting. New York, USA, 1992, 65-92.

[9] HSIAO C. T., CHAHINE G. L. Scaling of tip vortex cavitation inception noise with a bubble dynamics model accounting for nuclei size distribution[J]. Journal of Fluids Engineering, 2005, 127(1): 55-65.

[10] BENDAT J. S.,PIERSOL A. C. Random data: analysis and measurement procedures[M]. New York: Wiley, 1971.

[11] RANDALL R. B. Frequency analysis[M], 3rd Edition, Naerum, Denmark: Bruel and Kjaer, 1987.

[12] NEWLAND D. E. An introduction to random vibrations, spectral and wavelet analysis[M]. 3rd Edition, New York: Wiley, 1994.

[13] Wikipedia. http://en.wikipedia.org/wiki/Beaufort_scale

[14] ITTC Cavitation Committee Report[C]. 18th International Towing Tank Conference. Kobe, Japan, 1987.

10.1016/S1001-6058(11)60289-8

* Biography: LEE Jeung-Hoon (1978-), Male, Ph. D., Senior Research Engineer