| The prediction of hydrodynamic responses of ships advancing in waves is a classic research topic,which is of great significance for the design,operation and safety of ships.Over the past few decades,with the development of computer and related technologies,many numerical methods based on 3D potential theory have been developed to study the wave-body interactions.Now potential methods for zero-speed problems are relatively mature.But for forward speed cases,there are still some problems in computational stability and accuracy,and no reliable commercial software is available.So in this paper,numerical approaches for the hydrodynamic analysis of ships advancing in waves are systematically studied within the framework of potential flow theory in frequency domain.Compared to the time-domain method,the frequency-domain algorithm is more efficient,and its results can be directly used in the design of ship structures.The panel method based on the translating-pulsating Green's function is an important frequency-domain potential method for ship hydrodynamic problems with forward speed.Its computational precision depends on the number and type(flat or curved)of panels used to discretize the body surface,the variation(constant,linear or quadratic,et al.)of source or dipole strength over each panel and the accuracy of the influence coefficients(which are panel integrals related to the Green's function and its derivatives).In the past because the translating-pulsating Green's function is highly oscillatory,most of the researches about this method employed constant panels to discretize the body surface,which has some inherent shortcomings:the source distribution is discontinuous,accurate derivatives on boundaries are hard to be obtained and large numbers of panels are required.In view of this,the higher-order panel method is employed to investigate the forward-speed ship hydrodynamic problems in this paper.The Green's function used in the higher-order translating-pulsating source method and the nonconvergence problem of its panel integrals near the free surface are studied,and a semi-analytical quadrature is derived to improve the numerical stability.Besides,a frequency-domain higher-order hybrid Green's function method is established,so the calculation of the line integral on the waterline is avoided.The results of various ships under different conditions show that the hybrid method is more stable and accurate than the traditional methods.The higher-order panel method incorporated with translating-pulsating Green's function is first investigated.The Green's function is composed of Rankine source G~S and Froude-dependent component G~F.Through the analysis of the spatial distribution characteristics and panel integrals of the two components,it is found that G~S changes smoothly and its panel integrals can be calculated accurately,while G~F change violently along the horizontal direction and its panel integrals are hard to be accurately evaluated by using the traditional Gauss-Legendre quadrature.This inaccuracy leads to the instability of the above higher-order method in hydrodynamic calculations.To solve this problem,a semi-analytical scheme(which adopts a numerical quadrature for the integral along the vertical direction,while an analytical expression is derived for the integral along the horizontal direction)is established to calculate the panel integrals related to G~F in the integral equation.Based on this scheme,a semi-analytical higher-order translating-pulsating source method is developed and applied to calculate the hydrodynamic coefficients,wave-exciting forces and motion responses of various ships.Numerical results show that the semi-analytical higher-order method is more accurate and stable than the traditional constant panel method and higher-order translating-pulsating source method based on numerical quadrature.A frequency-domain hybrid Green's function method is further established.This method introduces an artificial control surface to decompose the fluid domain into an outer and an inner domains,where the translating-pulsating Green's function and Rankine source are adopted respectively(the former guarantees the radiation condition for any frequency and the later makes the method flexible to the free surface condition).To obtain more accurate results,steady flow effects are considered in inner free surface and body surface conditions.Based on the above method,a computer code is developed.Through the calculations of hydrodynamic forces and motion responses of different kinds of ships advancing in head waves,the hybrid method is proved to be stable and able to obtain better results than the traditional panel methods by using a relatively small computational domain with fewer discrete quantities.Then this hybrid method is applied to evaluate the 6-DOF motions and added resistance of ships with different headings.In oblique waves,an additional viscous roll damping coefficient is introduced into the motion equation.In the calculation of added resistance,a mixed method that combines the far-field and semi-empirical formulas is adopted so as to avoid the inaccuracy of classic far-field methods in short waves.Numerical simulations are conducted on the free motions and added resistance of S175 and a full formed bulk carrier S-Cb84 advancing with various headings.By comparing the computed and experimental results,it is found that motion responses in each direction are well estimated,and the present method is able to produce satisfactory prediction of added resistance in the whole frequency range.In conclusion,the frequency-domain potential methods established in this paper greatly increased the computational accuracy,stability and efficiency.The computer code based on the frequency-domain higher-order hybrid Green's function method can be applied to evaluate the hydrodynamic responses of different ship types under different conditions,and can be directly applied in the analysis of hull loads and hydroelasticity. |
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