A higher-order boundary element method(HOBEM)incorporated with analytical panel integrals related to translat-ing-pulsating source Green’s function is proposed for the hydrodynamic response prediction of ships advanc...A higher-order boundary element method(HOBEM)incorporated with analytical panel integrals related to translat-ing-pulsating source Green’s function is proposed for the hydrodynamic response prediction of ships advancing in waves.In this method,the 9-node bi-quadratic curvilinear elements employed to discretize the mixed-source/dipole boundary integral equation are mapped into the parametric plane through a coordinate transformation.Then in order to ease the numerical instability problem,a novel analytical quadrature is derived to calculate the influence coefficients by changing the integral order and using integration by parts.The singularity caused by infinite discontinuity is analyzed and eliminated by adopting some mathematical techniques.Through the calculations of panel integrals of Green’s function and its x-derivative,the analytical integral method is proved to be always accurate even for field points approaching the free surface,where numerical quadrature is impossible to give reasonable results.Based on this,a higher-order seakeeping program is developed and applied in the motion response prediction of two different types of ships(i.e.,a wall-sided ship Wigley III and a non-wall-sided ship S175).By comparing the computed results with the corresponding experimental data and numerical solutions of the translating-pulsating and higher-order Green’s function methods based on traditional Gauss quadrature,it is found that the HOBEM based on analytical quadrature is of better accuracy and stability.For the non-wall-sided ship,only the present method can produce reasonable pre-diction of motion responses,while obvious oscillatory phenomenon is observed in the results of the other two numerical methods based on Gauss quadrature.展开更多
Motion responses of two ships advancing parallel in waves with hydrodynamic interactions are investigated in this paper. Within the framework of the frequency-domain potential flow theory, a semi-analytical higher-ord...Motion responses of two ships advancing parallel in waves with hydrodynamic interactions are investigated in this paper. Within the framework of the frequency-domain potential flow theory, a semi-analytical higher-order translating-pulsating source(HOTP) method is presented to solve the problems of coupled radiation and diffraction potential. The method employs nine-node bi-quadratic curvilinear elements to discretize the boundary integral equations(BIEs) constructed over the mean wetted surface of the two ship hulls. In order to eliminate the numerical oscillation, analytical quadrature formulas are derived and adopted to evaluate the integrals related to the Froudedependent part of the Green’s function along the horizontal direction in the BIEs. Based on the method, a numerical program is originally coded. Through the calculations of hydrodynamic responses of single ships, the numerical implementation is proved successful. Then the validated program is applied in the investigations on the hydrodynamic interactions of two identical Wigley Ⅲ hulls and the underway replenishment of a frigate and a supply ship in waves with and without stagger, respectively. The comparison between the present computed results with experimental data and numerical solutions of other methods shows that the semi-analytical HOTP method is of higher accuracy than the pulsating source Green’s function method with speed correction and better stability than the traditional HOTP method based on Gauss quadrature. In addition, for two ships with obviously different dimensions,the influence of hydrodynamic interactions on the smaller ship is found to be more noticeable than that on the larger ship, which leads to the differences between the motions of frigate with and without the presence of supply ship.展开更多
Strongly nonlinear characteristics of ship roll owing to viscous effect can be usually observed. To describe the nonlinear roll behavior, the CFD method has been frequently employed with obvious advantages compared wi...Strongly nonlinear characteristics of ship roll owing to viscous effect can be usually observed. To describe the nonlinear roll behavior, the CFD method has been frequently employed with obvious advantages compared with the traditional semi-empirical formula method in estimating the roll damping. Numerical simulations of free decay and forced rolling at various forward speeds and amplitudes for a 3-D ship hull are conducted in the present research to predict ship roll damping, in which a RANS solver is employed and a dynamic mesh technique is adopted and discussed in detail. Numerical results, including nonlinear flow characters around ships, rolling decay curves and damping coefficients, show that they are all in good agreement with available experimental data. The linear and nonlinear damping coefficients are estimated and analyzed by fitting with exponential functions for various rolling amplitudes, frequencies and speeds in the free decay simulations, and the damping coefficients are obtained by a polynomial fitting in the forced roll simulations. It is indicated that the damping coefficients increase with increasing rolling angle amplitude and velocity. It is also emphasized that the effect of forward speed is significant to roll damping and the nonlinear damping decreases with increasing velocity.展开更多
基金financially supported by the National Natural Science Foundation of China (Grant No. 52101357)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 21KJB580012)the Scientific Research Start-up Fund of Jiangsu University of Science and Technology
文摘A higher-order boundary element method(HOBEM)incorporated with analytical panel integrals related to translat-ing-pulsating source Green’s function is proposed for the hydrodynamic response prediction of ships advancing in waves.In this method,the 9-node bi-quadratic curvilinear elements employed to discretize the mixed-source/dipole boundary integral equation are mapped into the parametric plane through a coordinate transformation.Then in order to ease the numerical instability problem,a novel analytical quadrature is derived to calculate the influence coefficients by changing the integral order and using integration by parts.The singularity caused by infinite discontinuity is analyzed and eliminated by adopting some mathematical techniques.Through the calculations of panel integrals of Green’s function and its x-derivative,the analytical integral method is proved to be always accurate even for field points approaching the free surface,where numerical quadrature is impossible to give reasonable results.Based on this,a higher-order seakeeping program is developed and applied in the motion response prediction of two different types of ships(i.e.,a wall-sided ship Wigley III and a non-wall-sided ship S175).By comparing the computed results with the corresponding experimental data and numerical solutions of the translating-pulsating and higher-order Green’s function methods based on traditional Gauss quadrature,it is found that the HOBEM based on analytical quadrature is of better accuracy and stability.For the non-wall-sided ship,only the present method can produce reasonable pre-diction of motion responses,while obvious oscillatory phenomenon is observed in the results of the other two numerical methods based on Gauss quadrature.
基金This work was financially supported by the National Natural Science Foundation of China(Grant No.52101357)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(Grant No.21KJB580012)the Scientific Research Start-up Fund of Jiangsu University of Science and Technology.
文摘Motion responses of two ships advancing parallel in waves with hydrodynamic interactions are investigated in this paper. Within the framework of the frequency-domain potential flow theory, a semi-analytical higher-order translating-pulsating source(HOTP) method is presented to solve the problems of coupled radiation and diffraction potential. The method employs nine-node bi-quadratic curvilinear elements to discretize the boundary integral equations(BIEs) constructed over the mean wetted surface of the two ship hulls. In order to eliminate the numerical oscillation, analytical quadrature formulas are derived and adopted to evaluate the integrals related to the Froudedependent part of the Green’s function along the horizontal direction in the BIEs. Based on the method, a numerical program is originally coded. Through the calculations of hydrodynamic responses of single ships, the numerical implementation is proved successful. Then the validated program is applied in the investigations on the hydrodynamic interactions of two identical Wigley Ⅲ hulls and the underway replenishment of a frigate and a supply ship in waves with and without stagger, respectively. The comparison between the present computed results with experimental data and numerical solutions of other methods shows that the semi-analytical HOTP method is of higher accuracy than the pulsating source Green’s function method with speed correction and better stability than the traditional HOTP method based on Gauss quadrature. In addition, for two ships with obviously different dimensions,the influence of hydrodynamic interactions on the smaller ship is found to be more noticeable than that on the larger ship, which leads to the differences between the motions of frigate with and without the presence of supply ship.
基金Project supported by the National Natural Science Foundation of China(Grant No.50639020)the National High Technology Research and Development Program of China(863Program,Grant No.2006AA09Z332)
文摘Strongly nonlinear characteristics of ship roll owing to viscous effect can be usually observed. To describe the nonlinear roll behavior, the CFD method has been frequently employed with obvious advantages compared with the traditional semi-empirical formula method in estimating the roll damping. Numerical simulations of free decay and forced rolling at various forward speeds and amplitudes for a 3-D ship hull are conducted in the present research to predict ship roll damping, in which a RANS solver is employed and a dynamic mesh technique is adopted and discussed in detail. Numerical results, including nonlinear flow characters around ships, rolling decay curves and damping coefficients, show that they are all in good agreement with available experimental data. The linear and nonlinear damping coefficients are estimated and analyzed by fitting with exponential functions for various rolling amplitudes, frequencies and speeds in the free decay simulations, and the damping coefficients are obtained by a polynomial fitting in the forced roll simulations. It is indicated that the damping coefficients increase with increasing rolling angle amplitude and velocity. It is also emphasized that the effect of forward speed is significant to roll damping and the nonlinear damping decreases with increasing velocity.
