对VLCC船基于理论和经验计算的波浪增阻预报修正方法杨春蕾;朱仁传;樊涛;周文俊;缪国平【摘要】文章基于一种新的理论方法和经验公式方法对波浪增阻进行预报,通过比较分析给出了一种改进的工程实用的计算公式.势流理论方法由于存在假设在短波增阻预报上精度不高,而经验方法的船型适用性不强.文中选取VLCC船迎浪航行为例,考虑吃水和航速影响进行了计算验证和比较分析.一种水平线段移动脉动源的三维面元法被用于求解速度势问题,进而采用三维船体辐射能量法得到船舶辐射增阻,基于二阶波浪力定常分量公式计算得到绕射增阻;经验方法采用ISO15016-2015推荐的STAWAVE2方法.通过辐射和绕射增阻曲线分析,对方法的适用性进行分析,进而对半经验方法的修正系数进行了研究,给出了反应相似船船型和航速特征的改进公式.【期刊名称】《船舶力学》【年(卷),期】2018(022)012【总页数】12页(P1483-1494)【关键词】辐射增阻;绕射增阻;格林函数;三维面元法;STAWAVE2方法【作者】杨春蕾;朱仁传;樊涛;周文俊;缪国平【作者单位】江南造船(集团)有限责任公司江南研究院, 上海 201913;上海交通大学船舶海洋与建筑工程学院,海洋工程国家重点实验室, 上海 200240;高新船舶与深海开发装备协同创新中心, 上海 200240;江南造船(集团)有限责任公司江南研究院, 上海 201913;上海交通大学船舶海洋与建筑工程学院,海洋工程国家重点实验室, 上海 200240;高新船舶与深海开发装备协同创新中心, 上海 200240;上海交通大学船舶海洋与建筑工程学院,海洋工程国家重点实验室, 上海 200240;高新船舶与深海开发装备协同创新中心, 上海 200240【正文语种】中文【中图分类】U661.30 IntroductionDue to the more stringent requirements of safety enhancement and emissions reduction,prediction of the added wave resistance of ships is getting more and more important.An assessment procedure for minimum power is provided in MEPC(Marine Environment Protection Committee)232(65)resolution,in order to maintain maneuverability in adverse conditions for ships,complying with EEDI(Energy Efficiency Design Index)regulation.The evaluation of EEDI has been enforced since 1 January 2013 in MEPC 232(65)resolution,regarding the Green House Gas emission of the navigation of ships.The effective consideration to improve EEDI index is achieved by reducing speed,but that will result in unconformity to the minimum power requirement which is calculated by minimum power lines,especially for large-scale ships.In such cases more accurate method for predicting the added resistance should be used.Conservative formulas for the added resistance are not applicable for the sophisticated consideration of requirements of two resolutions mentionedabove.Moreover,the accuracy of the added resistance is key to final EEDI report,which is obtained from correction data of sea trials based on ISO-15016:2015[1].Model tests can be conducted for the most reliable prediction when circumstances permit,but factors of cost and time preclude such tests.Therefore the investigation and validation on empirical and numerical methods are getting more and more important. Procedures recommended[2]for calculating added wave resistance by ITTC are adopted by ISO.The procedures include empirical methods from the STA-JIP(Sea Trial Analysis Joint Industry Project),namely STAWAVE1 and STAWAVE2,and the semi-theoretical method of the NMRI(National Maritime Research Institute).However,these methods are applicable to some extent to the ship type,draft,wave frequency and other factors.The Specialist Committee on Performance of Ships in Service(PSS Committee)[3]selected foregoing three methods and six type of ships to have comparison study for added resistance,and understand which method was the best method for the correction of speed/power trial.The results show that NMRI method combined with tank model in short waves gives the considerable accuracy.Returning to the reanalysis,the STAWAVE2 method would be convenient and preferred at the early design stage in the range of intermediate and short wave for the fine hull lines,because the empirical formulas for the diffraction resistance are relatively rational.NMRI(National Maritime Research Insititute)method has a better theoretical basis for the radiation resistance,and is more reasonably comprehensive for the diffraction resistance because of accommodation of correction of speed effect and waterline of the hull.NMRI method recommended by PSS,although better than most others,lacks transparencyand universalization in numerical method of 3D potential in the flow field and Kochin function.Note worthily,prediction of the added resistance in short waves at about λ/Lpp=0.3 relies on empirical parameters for the speed and draft effect whatever employing theoretical or empirical method.For a specialist ship,practical predictions are based on the in-house data relating to a similar basis ship.The difficulty of the accumulation of data is how to correct by the way of synergetic re-analyses of modern and older methods.At the framework of linear potential flow theory,two methods are available to estimate the added resistance:the far-field and near-field methods.The far field method was firstly introduced by Maruo[4]and derived the equation of steady second order force obtained by calculating the change of momentum for radiated wave energy.Joosen[5]revised the added resistance method based on Maruo method,and NMRI adopted the method for added resistance due to ship motions.Maruo method gives considerably accuracy for the cruiser stern ships,and does not apply the hull forms with bulbous bow.Joosen’s method improved the accuracy for the results of transom stern ships,but does not apply cruiser stern ships.Gerritsma[6]introduced the radiation energy method which is based on the far field method.Salvensen(1978)[7]investigated added resistance by calculating second order terms of disturbing forces andmoments.Strøm[8]evaluated these methods and gave the conclusion that the prediction of added resistance lied in the range of ship forms and speed.Faltinsen(1980)calculated added resistance by integrating pressureon average wetted surface of ship hull based on near field method with good validation results.It is important to note that the value of added resistance is a second order term,and the accurate prediction suits the exact solution of the motion response,which requires accurate solution of the velocity potential.Even though there is still controversy for the versatility and accuracy of the empirical approach of the ITTC,the method international organization is willing to promote such methods to improve due to the convenient and transparent calculation.For the practical prediction for the designers,the correction empirical formulas are established from tank tests data and theoretical results.Jinkine[9]developed an estimation formula of added resistance including the principle dimension of ships for the long wave length,however the value for the short wave length should be corrected.Havelock[10]derived the steady drag formula for the fixed vertical cylinders.Fujii[11]established semi-empirical formulas for the diffraction resistance based on Havelock.Kuroda[12-13]further corrected the Fujii formula.MARIN[14]calculated the added resistance due to diffraction and radiation relating to Jinkine method,and formed a basis for STAVWAVE2 method.Though the empirical formulas give considerable accuracy,estimation based on in-house database is important.In this paper,based on the existing data of the basis ships in Jiangnan shipyard,the theoretical and the empirical methods are investigated in order to establish the improved model for predicting the added resistance with better accuracy and reliability for the VLCC type ship.A 3-D panelmethod based on the horizontal line segment translating and pulsating source panel is used to solve potential problem,and added resistance due to the radiation is obtained by 3D radiation energy method for ships,while one due to the diffraction is obtained by the second order steady-state force formula.STAWAVE2 method is adopted as the semi-empirical parable study is conducted and advantage of different methods is analyzed.Revised formulas reflecting the characteristic of VLCC are validated with good agreement with experimental data.1 Theories of potential flow and added resistance1.1 Potential flow theoryA right-handed orthogonal coordinate system fixed in the mean position of the ship with the x-axis in the direction of constant forward speed,and the z-axis vertically upwards through the center of ship gravity is considered.The ship is advancing at a constant mean forward speed U0in sinusoidal regular waves with an arbitrary heading.Assuming the fluid is ideal,fluid motions are irrotational and potential flow theory can be applied to describe the wave.The total spatial velocity potential is decomposed:where φ0is the incident wave potential,φ7is the diffraction potential of the fixed ship,ωeis encounter frequency,φjis the normalized velocity potential due to radiated motions in six degrees of freedom,is the complex amplitude of the j-th degree of freedom.φ0is given by:where A is amplitude of the incident wave,ω0is circular frequency,k is wave number,H is the water depth,β is the incident wave angle.For diffraction and radiation wave potential,the boundary value problem to be solved is:where U0is the ship speed,mjis the m-term,which represents the interaction between the steady forward motion and the periodic oscillatory motion of ships.By assuming that the steady potential is small,a simplified m-term can be written as:(m1,m2,m3)=(0,0,0 )and(m4,m5,m6)=(0,U0n3,-U0n2).To solve the boundary value problem,the mixed source and dipole distribution model[15]and 3D translating&pulsating source Green’s function(3DTP)are used.And the boundary integral equation can be written as:where α is solid angle of field point,P( x,y, z )is field point,Q( ξ,η, ζ)is source point,SB is average wetted surface of ship hull,wl is waterline.The Green’s function is expressed[16-17]by:whereFor the treatment of integrati on on the panel ΔSj,a more effective integration of horizon-tal line segment is used,as Fig.1 shown.The panel integration of the G*(P, )Q and its differential is converted into line integration:Fig.1 Discretization of a panelwhere M is the number of hor izontal line segments,αjis the weight coefficient of the j-th segment which is decided by the integral method used in vertical direction.The line segment integrationthe differentialandare expressed analytically shown in Ref.[16].Fig.2 shows hull lines and panel grids of KVLCC.Fig.2 Hull lines and panel grids of KVLCCRadiation and diffraction potential could be obtained by carrying out calculations for boundary element method(BEM).Withφjknown,hydrodynamic coefficient such as added mass μjkand damping λjkc an be obtained.Wave forces including incident force )and diffraction force)are calculated separately by using respective potential φ0andφ7.Corresponding equation for motions can be given aswhere mkjis inertia matrix,and Cjkis hydrostatic restoring terms.1.2 Added resistance due to radiationIn principle of energy conservation,the radiation energy of an encounter period delivered by the ship should equal to the work done by average added resistance acting on ship hull.Radiation energy method of 3D BEM can be derived with reference of that based on strip method.This added resistance can be expressed as a function of hydrodynamic coefficient:When the speed is zero,Ajk=Ak j,the first term in the parentheses shouldbe taken as zero.Thenwhere XkRand XkIare real part and imagine part of the complex amplitude of ship motion in k-th degree of freedom.The above equation is consistent with the Joosen method[5]for the zero speed ship.1.3 Added resistance due to diffractionIt is assumed for ships that the disturbance potential is small compared to the incident potential (φ Bpp φ0),and therefore the second-order force of steady state derived based on Salvensen[7]can be expressed by:where β is wave angle,is complex conjugate of φ0,φBis body disturbing potential.When an interaction between radiation and diffraction potential is ignored,the added resistance due to diffraction can be given as follows:2 STAWAVE2 method2.1 Estimation for added resistance due to radiationSTAWAVE2 method is based on Jinkine method[9],and an approximate formula of nondimensional coefficient of added resistance due to radiation is as follows:Then the added resistance is:where a1=60.3and a2=Fn1.5exp(-3 .5Fn)account for the effects of the speed and principal dimensions for the peak value of radiationresistance.andresponse to inclination of the curve for the added resistance.Lpp,B,kyyand ζ are ship length,breadth,radius of gyration in lateral direction and wave amplitude,respectively. ω/1.17 is non-dimensional frequency,when=1,the added resistance is a minimum value.,and Cbis block coefficient.After the verification of practical calculations,it is found that the peak of added resistance moves to the area of longer wave with a higher varying speed.2.2 Estimation for added resistance due to diffractionA semi-empirical formula based on Takahashi method[19-20]for calculating the diffraction added resistance is adopted,and the non-dimensional coefficient is:Added resistance due to diffraction is:whereis used to correspond to the effect of speed,draught and characteristic of hull forms.I1is modified Bessel function of the first kind of order 1,K1is modified Bessel function of the second kind of order 1,TMis the mean draught.Fig.3 shows the effects of draft and wave-length on added resistance due to diffraction.Ref.[12]refers to bulk carrier and container ships,validation of the data distributes the range of α1(keTM)～α1(1. 5keTM ).Ref.[20]refers to the different range of α1(0. 74keTM )～α1(1. 0keTM)for the tankers,and the range of α1(0. 56k eTM )～α1(1.0keTM)where radiation added resistance predominates for container ships.Fig.3 Comparison of the effects of draft and wave length3 Comparisons of theory and empirical formulasThe different methods are used to validate two tankers,one is KVLCC2 which is a standard ship model for CFD validation,and another is a VLCC which is a built hull.The accuracy and applicable range will be analyzed by comparing tank test data and computed results.Main dimensions are presented in Tab.1.Tab.1 Main dimension of ships?3.1 Added resistance analysisThe heave and pitch motions are shown in Fig.4(a)and(b)based on 3D frequency domain method.The motion response results are in good agreement with experiment data.Fig.4 RAOThe results of added resistance at the speed of Fn=0.142 for KVLCC2 are shown in Fig.5,and the experimental data is from NTUA and INSEAN.Based on the analysis of theoretical and numerical calculation and comparisons with test data,it is concluded that:(1)As shown in Fig.5(a)the theoretical results of Rawin the range of λ/Lpp＞0.7 and the resonance frequency range are in good agreement with experimental data,but the added resistance due to short wave is inaccurate;the empirical formulas enable a reasonably accurate prediction for Raw in the range of λ/Lpp＜0.5,but resonance frequency range is not given a reasonable estimation.(2)As shown in Fig.5(b)the range of the maximum resistance obtained by SATWAVE2 method is in the lower frequency range;the added resistancesin the range of λ/Lpp＜0.5 for theory and STAWAVE2 are 25%-30%less than experimental data.The advantage of 3D translating and pulsating source method is that free surface condition is satisfied automatically and the dispersed error can be reduced.However,the viscous and nonlinear effects are great and not captured by potential flow theory,especially for full hull forms,moreover the major component at short-wavelengths is the diffraction resistance.Though the panel density is increased to improve the numerical accuracy,it is very difficult to accurately predict in short wavelength range.For the VLCC,the relative wave length is short in the condition of the actual sea trial and service operation.The foregoing results show that the theoretical method has a limitation and empirical method is crude for the prediction of the added resistance in short waves.The direct measurement to improve the accuracy is that more parameters are included in the formulas in order to represent the hull forms better.One alternative measurement is provided by adjusting the parameters of formulas applicable to geosim ships.Fig.5 Added resistance at different speeds3.2 Different component analysisFig.6 shows the results of two different components of the added resistance by using two methods.It can be observed that the peak values of ordinate are at λ/Lpp=0.5 and λ/Lpp=1.0 respectively for theoretical and empirical methods.The added resistance due to diffraction is the main component,so the main reason for underestimating the added resistancein short waves is due to the fact that the diffraction resistance is less than that experiment values.The maximum of radiation resistance of empirical results occurs at lower frequency than indicated by theory results.The peak value is influenced by the radiation resistance.In fact the uncertainty in the added resistance measurements is larger[14],especially for low speed ships,so it is difficult to obtain accurate results in the short wave range.For practical predictions,adequate margin is necessary.Other numerical method such as CFD is influenced by grid density and is limited to predict the short wave resistance.It is technically feasible to improve the existed methods based on the analysis of theoretical and semi-empirical methods and tank test data.Fig.6 Compenents of added resistance3.3 Revised STAWAVE2 methodAn improved expression for radiation resistance can be found to improve the accuracy of prediction according to comparable analysis of calculated results and test data.The formula is given as:The coefficients of b1and d1in Eq.(12)can be adjusted to agree the test data better,like the correction of Rob[14],but the database from different institute may be different.The equation fitted by calculated results can be expressed by:Eq.(14)is limited to extend to the prediction for modern VLCC because it is applicable to the blunt bow shape at low speed,and meets the assumptionof vertical plane barrier.A blunt coefficient which reflects waterline shape can be used to improve the accuracy of prediction,but the practical calculation for this coefficient is not easy and actual ship data of different ship type is fluctuated.The following equation can be given through a number of numerical tests:As is expected,it is seen the added resistance in a wide range of wavelength is in good agreement with experimental data,and the maximum added resistances occur at reasonable wavelengths for two ships.The added resistance of STA2 correction method is shown in Fig.7. Fig.7 Added resistance of STA2 correction methodIn order to validate the applicability to the draught effect,the VLCC case in the ballast condition(T=10 m)is chosen.The performance of VLCC navigation in the ballast condition is often needed for ship owners.For the case of Fr=0.144,results of theoretical and corrected STAWAVE2 method are shown in Fig.8.It is seen that present correction results agree well with the experiment values.It is stressed that the present empirical method is limited to the geosim ships of VLCC type.Fig.8 Added resistance of VLCC at ballast draft4 ConclusionsHydrodynamic coefficients and wave forces are solved by 3-D panel method based on the horizontal line segment translating and pulsating source panel,and added resistance due to the radiation is obtained by 3D radiation energy method for ships,while one due to the diffraction isobtained by the second order steady-state force formula.STAWAVE2 method recommended by ISO15016-2015 is adopted as the semi-empirical method.Improved formulas are presented based on analysis of calculated results.Conclusions are summarized:(1)Theoretical results indicate that the maximum of added resistance agrees with experi-mental data,but underestimate the added resistance in the relative short wave range.The modern numerical method based on line integration is shown a higher efficiency than traditional BEM.In this paper,the hull is divided into discrete elements of 1 300,and cases are computed on a computer with Intel Core I5(3.2 GHz).For each frequency calculation,about 3.9 minutes are needed.(2)The differences between the results of STAWAVE2 and experiment method are large.Improved formulas are presented and the results based on these formulas demonstrate the good agreement can be achieved for VLCC.It can be used to accumulate the database for seakeeping performance.(3)The present theoretical method predicts the added resistance with good accuracy and high efficiency in the range of medium and long wave for variable speeds and drafts.A notable discrepancy between theory and experiment was found in the range of short wave.References【相关文献】[1]IMO MEPC 68/INF.14 2015 Ships and marine technology-Guidelines for the assessment of speed and power performance by analysis of speed trial data[S].2015.[2]ITTC 7.5-04-01-01.2 ITTC-Recommended procedures and guidelines analysis of speed/power trial data[R].2014.[3]ITTC Specialist committee on performance of ships in service-final report and recommendations to 27th ITTC[C].Proceedings of 27th ITTC-Volume III,2014.[4]Maruo H.The excess resistance of a ship in rough seas[J].International Shipbuilding Progress,1957,4(35):337-345.[5]Joosen W P A.Added resistance in waves[C]//Proceedings of the 6th Symposium on Naval Hydrodynamics.Washington,USA,1966.[6]Gerritsma J,Beukelman W.Analysis of the resistance increase in waves of a fast cargo ship[J].International Shipbuilding Progress,1972,19(217):285-293.[7]Salvensen N.Added resistance of ships in waves[J].Journal ofHydronautics,1978,12(1):24-34.[8]Strøm-Tejsen J,Yeh H Y H,Moran D D.Added resistance in waves[J].Transactions of the Society of Naval Architects and Marine Engineers,1973,81:109-143.[9]Jinkine V,Ferdinande V.A method for predicting the added resistance of fast cargo ships in head waves[R].Institute of Office of Naval Architecture,Belgium,1973:1-40. 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