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(China Ship Scientific Research Center,Shanghai 200011,China)

Influence of Added Wave Resistance Calculation Methods on Ship Speed in Seas

WANG Yan-xia,WANG Shan,CHEN Jing-pu

(China Ship Scientific Research Center,Shanghai 200011,China)

fwis one of the factor in EEDI formula.This paper studies the influence of different added wave resistance calculation methods on ship speed in representative sea condition.The using three theoretical models is realized to calculate the added resistance,and comparing the calculation results with model test.The results from the three models show that all the decrease of ship speed from three theoretical models are higher than the model test results in waves,which lead to lowerfw;Model-3 may overestimate the added resistance in irregular wave;thefwobtaining from Model-1 and Model-2 is close to the one from model tests in waves.

fw;added wave resistances;representative sea conditions;ship speed

0 Introduction

With the entry into force of the 2012 guidelines on the methods of calculation of the attained Energy Efficiency Design Index(EEDI)for new ships,the technology demand of energy saving and emission reduction become more and more urgent,thus great changes have taken place from ship design to supporting facilities.These changes mainly embody the four aspects as follows:(1)Optimization design technologies[1-3]are continuously improved for ship hull, propeller and rudder,etc.(2)Ship hydrodynamic energy saving device[4]becomes the focus of ship research and application area.(3)Large scale and low consumption becomes the tendency of main engine design.(4)Utilization and development of renewable energy[5]arouses researcher’s attention.

One of the changes in optimization design technologies of ship hull is objective function, which is from the single hydrodynamic one in calm water to the multi-hydrodynamic ones not only in calm water but also in waves and winds.Such change relates to the higher demand of integrative hydrodynamic performance coming from shipping industry,and also relates to the coefficient indicating the decrease of speed(fw)factor in EEDI formula.At the present stage, the value of fw is one,because the calculation methods of fw have not been unified internationally.Once the methods of fw have been unified,the value for attained EEDI calculated by the EEDI formula using the obtained fw should be referred to EEDIweather,which is suggested tobe indicated in the EEDI Technical File to distinguish it from the EEDI value.

The key to obtain fw is the calculating of added resistance due to waves.Now more and more numerical methods have been developed to calculate the added resistance due to waves[6]. Among those,two new methods[7-8]have been put forward at Marine Environment Protection Committee 65th session(‘MEPC65’),which is used to calculate the coefficient of decrease in ship speed included in EEDI formula.And IMO suggests the two sponsors cooperate to examine the proposed technology with a view to unify the guidelines and submit the outcome to the next session.Meanwhile,ITTC Recommended Procedures and Guidelines[9]suggest a more simpler empirical formula.

This paper is organized as follows:Chapter 1 briefly introduces the three theoretical methods.In Chapter 2,two large slow ships with very blunt bow shapes,which have higher added resistance due to waves,are chosen to analyze the influence of added resistance on the ship speed and fw.Added resistance coefficient in regular waves resulting from different methods are compared,and then based on the added resistance in irregular waves,ship speed in waves and winds are predicted.Finally,in Chapter 3 we present conclusions and some perspectives.

1 Theoretical models

In this paper,added resistance due to wavesis calculated by three theoretical methods,which are shown in Tab.1.

Model-1 and Model-2 both need to calculate the added resistance coefficientshown in Eq.(1),where Rwaveis added resistance in regular waves.The obvious difference between Model-1 and Model-2 lies in the calculation method of Rwave.Model-1 mixes numerical calculations and model tests,while model-2 adopts a pure numerical method.Added resistance in irregular waves ΔRwavecan also be calculated by linear superposition of the frequency spectrumand added resistance in regular wavesas Eq.(2).

where ρ is the water density,g is the gravitational acceleration,ζais the amplitude of incident regular waves,B is the ship breadth in meters,Lppis the length between perpendiculars,and Sζis expressed as follows:

Compared with Model-1 and Model-2,Model-3 is a simple experiential formula,which does not need to calculate the added resistance coefficient.

Tab.1 Comparison of theoretical methods

1.1 Model-1[7]

Added resistance in regular waves Rwaveis calculated from the components of added resistance primary induced by ship motion in regular waves Rwmand added resistance due to wave reflection in regular waves Rwr.

where Rwmis calculated based on Maruo theory[10],while added resistance due to wave reflection in regular waves Rwris calculated as follows:

where ζais amplitude of regular waves;B is ship breadth;V is ship speed;Bfis bluntness coefficient,which is derived from the shape of water plane and wave direction;Cu is coefficient of advance speed,which is determined by a tank test in regular waves;K is wave number of regular waves;d is ship draft;I1is modified Bessel function of the first kind of order 1;K1is modified Bessel function of the second kind of order 1;and α is angle between ship course and regular waves;and ω is circular frequency of incident regular waves.

1.2 Model-2[8]

Added resistance in regular waves Rwaveis calculated as Eq.(3),while Rwmis calculated based on Gerritsma and Beucklman(1972)[11],added resistance due to wave reflection in regular waves is calculated using the formula proposed by Duan and Li(2003)[12].

where a,b and c are bluntness coefficients,which are determined by the shape of water plane.

1.3 Model-3[9]

A dedicated and simplified method has been developed by ITTC recommended procedures and guidelines(2012)to estimate the added resistance in waves with limited input data.

where HW1/3is the significant wave height,LBWLis the distance of the bow to 95%of maximum breadth on the waterline.The restrictions are:HW1/3＜0.015LPP,wave induced motion is small(pitch<0.5°,roll<1°),wave direction is heading(within 0°to±45°).

2 Influence of added resistance on ship speed in waves and winds condition

2.1 The comparison of added resistance coefficients in regular waves

In order to study the influence of added resistance on ship speed,this paper chooses two large slow ships with very blunt bow shapes as typical examples,which have higher added resistance due to waves.Main parameters of the two ships are listed in Tab.2,and the draft is scantling one,which is consistent with EEDI calculation condition.

Fig.1 and Fig.2 show the comparison of added resistance coefficient of theoretical calculations with model tests for tanker-1 and tanker-2,respectively.Each ship shows the results at speed of 13 kns and 15.5 kns.

Tab.2 Main parameters

Fig.1 Comparison of added resistance coefficient in regular waves for tanker-1

Fig.2 Comparison of added resistance coefficient in regular waves for tanker-2

As we can see from Fig.1,at the speed of 13 kns and 15.5 kns,the peak values of added resistance coefficient calculated by numerical method are located near λ/Lpp≈1.2,while the model test results are located near λ/Lpp=1.And the peak value of Model-1 is the biggest,the model test is the smallest.In short waves(λ/Lpp＜0.5),the results calculated by Model-1 andModel-2 are close,which are higher than model tests at the speed of both 13 kns and 15.5 kns.

As we can see from Fig.2,it presents similar rules to Fig.1 about the peak values of added resistance coefficient at 13 kns,but at 15.5 kns it is not similar.It shows that all of the results are close in short waves(λ/Lpp＜0.5).

2.2 Influence of ship speed and decrease of ship speed

Based on the results from Chapter 2.1,the added resistance in irregular waves can be calculated using the frequency spectrum showed in Chapter 1.And added resistance due to winds is calculated by the following formula on the basis of the mean wind speed and wind direction.

where,relative wind velocity VR=V-Vwind×cosγ,air density ρa(bǔ)=1.225 kg/m3,wind-resistance coefficient Cx=0.8,ATis projected transverse area above the designated load condition.

As the two ships is above 150 meters in length,so we choose Beaufort scale 6 as the input data,which is consistent with calculation condition of fw in EEDI formula.The parameters of representative sea condition are listed in Tab.3.

Then deliver power(Pds)can be obtained with of different models and model tests.The results are shown in Fig.3 for two ships.Pds1,Pds2 and Pds3 mean the deliver powers obtained from Model-1,Model-2,Model-3,respectively.And Pds0 and Pds4 are deliver powers in calm water and in waves model tests,respectively.The influence of ship speed and decrease of ship speed(fw)are listed in Tab.4.It can be seen that:

(1)For tanker-1,the ship speed in calm water and in representative sea condition is 15. 09 kns and 13.46 kns from model test results,which shows that the decrease of speed is about 1.63 kns and fw is 0.89.For tanker-2,the decrease of speed is about 1.37 kns and fw is 0.91.

(2)Among the theoretical results,the decrease of ship speed resulting from Model-3 is the highest.On the other side,the decreases of ship speed resulting from Model-1 and Model-2 are very close,so does the fw.

(3)As to tanker-1,the decreases of ship speed for Model-1 and Model-2 are about 1.87 kns and 1.79 kns respectively,which show that it is about 0.24 kns and 0.16 kns higher than the model test results in waves,while the deviation of fw is only about 1%.It has the similar characteristic to tanker-2.

(4)The deviation of decrease of ship speed is about 0.8 kns between Model-3 and model test results in waves for tanker-1,and the deviation of fw is about 5%.So does it for tanker-2.Such conclusion may be obtained that Model-3 overestimates the added resistance in irregular wave.

Tab.3 Representative sea condition for ships

Fig.3 Deliver power of different models and model test(Left:tanker-1;Right:tanker-2)

Tab.4 Influence of ship speed and decrease of ship speed(fw)

3 Conclusions

In this paper,three different methods of added resistance calculation are introduced briefly and applied to assess the added resistance of two tankers,which are compared to the model test results.Based the above calculations and analysis,some conclusions are obtained as follows:

(1)Comparison with the model test results in waves,all the decrease of ship speed from three theoretical models are higher,which lead to lower fw.

(2)Among the theoretical results,the decrease of ship speed resulting from Model-3 is the highest,so Model-3 may overestimate the added resistance in irregular wave.On the other side,the decreases of ship speed resulting from Model-1 and Model-2 are very close,so do the fw.

(3)The deviation of decreases of ship speed obtained from both theoretical models(Model-1 and Model-2)and model test in waves is 0.11-0.25 kns,while the deviation of fw is only about 1%.

(4)The deviation of decreases of ship speed obtained from the theoretical Model-3 and model test in waves is about 0.8 kns for two tankers,while the deviation of fw is about 5%.

(5)The results also show that great difference exists in the above three Models themselves, and each of them has its individual characteristic and calculation precision.

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波浪增阻計(jì)算方法對(duì)船舶航速的影響分析

王艷霞，王 杉，陳京普

（中國(guó)船舶科學(xué)研究中心，上海200011）

失速系數(shù)（fw）是EEDI公式的計(jì)算參數(shù)之一。文章研究了典型海況下不同的波浪增阻計(jì)算方法對(duì)船舶航速以及fw的影響。文中主要基于三種波浪增阻理論計(jì)算模型，以肥大型船為研究對(duì)象，計(jì)算分析典型海況蒲氏六級(jí)下的波浪增阻系數(shù)的分布規(guī)律以及相同收到功率下的航速和fw。結(jié)果表明：三個(gè)理論模型計(jì)算得到的fw均低于模型試驗(yàn)結(jié)果；Model-3高估了不規(guī)則波中的波浪增阻值；Model-1和Model-2計(jì)算得到的fw與模型試驗(yàn)結(jié)果較接近。

EEDI；fw；波浪增阻；典型海況；船舶航速

U661.31

:A

王艷霞（1980-），女，中國(guó)船舶科學(xué)研究中心高級(jí)工程師，E-mail：wangyanxia@702sh.com；

U661.31

:A

10.3969/j.issn.1007-7294.2016.03.003

1007-7294（2016）03-0258-07

王 杉（1990-），男，中國(guó)船舶科學(xué)研究中心工程師；

陳京普（1982-），男，中國(guó)船舶科學(xué)研究中心高級(jí)工程師。

Received date：2015-09-06

Biography：WANG Yan-xia(1980-),female,senoir engineer,E-mail:wangyanxia@702sh.com;

WANG Shan(1990-),male,engineer.