| The capability of ships to sustain speed in a seaway is one of primary objectives which should be taken into account in the design stage.Compared with that in calm water,the resistance acting on ships advancing in waves increases.Added resistance represents the margin of the latter over the former,which is induced by winds or waves.It effects not only navigational performance of ship advancing in waves with design speed,but also the selection of power system and propulsion system.In addition,added resistance is also the key to the calculation of ocean factor f_w in EEDI formula presented by IMO.In seakeeping calculation,added resistance is a kind of second order wave force,which is caused by complicated factors.So developing an accurate and effective approach to predict and analyze added resistance of ships advancing in waves is valuable and significant both in theory and in practice.Good prediction of added resistance is based on accurate evaluation of ship motion and first order hydrodynamic forces.In current engineering,for frequency domain hydrodynamic calculation of ships advancing in waves,no robust commericail software based on 3D translating and pulsating source Green's function(3DTP)method is available,only some approximation methods are adopted such as strip theory and 3D pulsating source Green's function method(3DP)with velocity approximation.This is mainly caused by the lack of stable and effective approach to evaluate 3DTP and its partial derivatives.In the paper,the hydrodynamic forces and motions of ship advancing in waves are estimated by using 3D frequency domain potential flow theories.The integral character of 3D translating and pulsating point source Green's function in Havelock type is studied.Singularities and difficulties in calculation of 3DTP-PS are analyzed and overcame by using LOBATTO rule and integration by parts.A semi-analytical expression of 3DTP distributing along line segment(3DTP-LS)is outlined and derived by exchanging the order of integration in physical space and Fourier space.Compared with 3DTP-PS,both the order of infinity multiplier and the amplitude of oscillation function decrease,and the term with infinity number vanishes as well.3DTP-LS is better for rapid and effective numerical calculation.To obtain the integral of 3DTP Green's function over a panel,a new integral scheme is established based on3DTP-LS.Numerical results show that this new scheme is more efficient and accurate than normal Gaussian integral method,especially when both of the source point and field point are close to free surface.Added wave resistance is mainly categorized into the contributions of radiation and diffraction.Based on the principle of radiation energy,connection between added resistance and radiation energy is established and a new 3D radiation energy method is proposed.Compared with tranditional radiation energy method,the new method builds the connection between added resistance and 3D frequency hydrodynamic results and it is simpler and more practical.The diffraction added resistance is calculated by using the method based on second order steady-state force formula.Theoritically,the present method can predict added resistance of ships advancing in waves with any encounter frequency.Corresponding codes are programmed and a potential solver called ShipRaw for hydrodynamic calculation and added resistance is developed.A mathematical ship-Wigley III,a senlder ship-S175 container ship and a blunt ship–KVLCC2 are selected for numerical calculations of hydrodynamic coefficients,motions and added resistance.Numerical results are validated for the model by comparing them with experimental data.Reasonable added resistanc can be obtained by the present method for all the three ships,and discrepancy between numerical results and experiment data can be only observed for blunt ships advancing in short waves.Components analysis of added resistance is also carried out.The ratio of radiation and diffraction added resistance are obtained with various wave frequencies.It also indicates that ShipRaw can also be used for ships advancing in oblique waves.According to the advantages of present method and empirical formula,a mixed method is established to predict added resistance of blunt ships.Added resistance of KVLCC2 and an oil tanker are calculated by use of the mixed method.Numerical results indicate that the accuracy in the calculation of added resistance in short waves can be improved by use of the mixed method.According to wave spectrum,spectral analysis method is adopted to predict the average added resistance of ships advancing in irregular waves.Average added resistance of S175advancing in irregular waves is predicted.Numerical result agree well with experiment data.Furthermore,the influences of significant wave height,average period,forward speed,wave spectrum and wave angle on average added resistance are investigated.For blunt ship advancing in high sea state,correction of added resistance in regular short waves by use of empirical formula is conducive to the prediction of average added resistance. |
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