The singularities, oscillatory performances and the contributing factors to the 3-＇D translating-pulsating source Green function of deep-water Havelock form which consists of a local disturbance part and a far-field ...The singularities, oscillatory performances and the contributing factors to the 3-＇D translating-pulsating source Green function of deep-water Havelock form which consists of a local disturbance part and a far-field wave-like part, are analyzed systematically. Relative numerical integral methods about the two parts are presented in this paper. An improved method based on LOBATTO rule is used to eliminate singularities caused respectively by infinite discontinuity and jump discontinuous node from the local disturbance part function, which makes the improvement of calculation efficiency and accuracy possible. And variable substitution is applied to remove the singularity existing at the end of the integral interval of the far-field wave-like part function. Two auxiliary techniques such as valid interval calculation and local refinement of integral steps technique in narrow zones near false singularities are applied so as to avoid unnecessary integration of invalid interval and improve integral accordance. Numerical test results have proved the efficiency and accuracy in these integral methods that thus can be applied to calculate hydrodynamic performance of floating structures moving in waves.展开更多
Based on the second order hydroelasticity theory of ships, the numerical methods and the calculated results of the non-linear hydroelastic responses of a ship traveling in rough seas were investigated. The non-linear ...Based on the second order hydroelasticity theory of ships, the numerical methods and the calculated results of the non-linear hydroelastic responses of a ship traveling in rough seas were investigated. The non-linear hydrodynamic actions induced by the rigid body rotations and the variations of instantaneous wetted surface area were included in the second order analysis. The first order wave potentials and responses, which are sure to make the major contributions to the second order hydrodynamic actions, were obtained by employing the translating and pulsating source Green function and the Kelvin steady wave flow solution based on the linear three-dimensional hydroelasticity theory. The influences of the forward speed and the steady wave flow on the responses, and the differences of the predicted non-linear responses were illustrated by the numerical examples of a SWATH ship traveling with forward speed of 12 kn in irregular waves.展开更多
The singularities and oscillatory performance of translating-pulsating source Green＇s function in Bessho form were analyzed. Relative numerical integration methods such as Gaussian quadrature rule, variable substitut...The singularities and oscillatory performance of translating-pulsating source Green＇s function in Bessho form were analyzed. Relative numerical integration methods such as Gaussian quadrature rule, variable substitution method （VSM）, and steepest descent integration method （SDIM） were used to evaluate this type of Green＇s function. For SDIM, the complex domain was restricted only on the 0-plane. Meanwhile, the integral along the real axis was computed by use of the VSM to avoid the complication of a numerical search of the steepest descent line. Furthermore, the steepest descent line was represented by the B-spline function. Based on this representation, a new self-compatible integration method corresponding to parametric t was established. The numerical method was validated through comparison with other existing results, and was shown to be efficient and reliable in the calculation of the velocity potentials for the 3D seakeeping and hydrodynamic performance of floating struc- tures moving in waves.展开更多
Based on the 3-D surface panel method combined with the translating-pulsating source Green function, an approximate approach is developed to solve the hydrodynamic interacting problem of multiple ships advancing paral...Based on the 3-D surface panel method combined with the translating-pulsating source Green function, an approximate approach is developed to solve the hydrodynamic interacting problem of multiple ships advancing parallel in waves. Focus is on improving the calculating efficiency. In this approach, each ship is assumed to be in each other＇s far-field, and the near-field term in this Green function is neglected if the source point falls on one ship and the field point on others. Further, a matching relationship between the far-field waves and the interfered regions, which are defined as the overlapping areas between the mean wetted body surface of one ship and the propagating regions of the waves generated by another ship, is introduced to avoid the unnecessary computation of the relative terms of the Green function, if the field point is not in the overlapping areas. The approach is validated through studying the hydrodynamic terms and the free motions of two or three ships in side-by-side arrangement by comparing the obtained results with the model tests and the predictions of the exact method. The average calculating speed for the present approximate method is about 1.65-1.8 times of that for the exact method for solving the hydrodynamic interaction problem of two ships, and 2.56-2.73 times for that of three ships.展开更多
A new mathematical integral representation including five integrals about the far field wave shape fimction of Havelock form translating-pulsating source is obtained by performing variable substitution. Constant-phase...A new mathematical integral representation including five integrals about the far field wave shape fimction of Havelock form translating-pulsating source is obtained by performing variable substitution. Constant-phase curves and propagation wave patterns are investigated by applying stationary phase analysis method to the new representation. Some findings are summarized as follows： （1） when 0〈r 〈0.25 （where r is the Strouhal number）, three types of stationary phase curves corresponding to three propagation wave patterns such as fan wave pattern, inner V and outer V wave patterns, are found in the integral representation. （2） When r 〉0.25, besides three types of wave patterns such as a ring-faning wave pattern, a fan wave pattern and an inner V wave pattern, a new one called parallel wave pattern is also found which not only exists in the integrals about the ring-fan wave and fan wave, but also in the integrals whose interval is [0, 7＇] ~ In addition, Characteristics about these parallel waves such as mathematical expressions, existence conditions, propagation directions and wave lengths are obtained, and cancellation relationships between these parallel waves are stated, which certificates the fact that there are no parallel waves existing in the far field.展开更多
In order to interpret the physical feature of Bessho form translating-pulsating source Green function, the phase function is extracted from the integral representation and stationary-phase analysis is carried out in t...In order to interpret the physical feature of Bessho form translating-pulsating source Green function, the phase function is extracted from the integral representation and stationary-phase analysis is carried out in this paper. The complex characteristics of the integral variable and segmentation of the integral intervals are discussed in m complex plane. In θ space, the interval [-π/2+φ,-π/2+φ-iε] is dominant in the near-field flow, and there is a one-to-one correspondence between the real intervals in m space and the unsteady wave patterns in far field. If 4τ>1(τ is the Brard number), there are three kinds of propagation wave patterns such as ring-fan wave pattern, fan wave pattern and inner V wave pattern, and if 0<4τ<1, a ring wave pattern, an outer V and inner V wave pattern are presented in far field. The ring-fan or ring wave pattern corresponds to the interval [-π+α,-π/2+φ] for integral terms about k2, and the fan or outer V wave pattern and inner V wave pattern correspond to [-π+α,-π/2) and(-π/2,-π/2+φ] respectively for terms about k1. Numerical result shows that it is beneficial to decompose the unsteady wave patterns under the condition of τ≠0 by converting the integral variable θ to m. In addition, the constant-phase curve equations are derived when the source is performing only pulsating or translating.展开更多
In the framework of 3D potential flow theory, Bessho form translating-pulsating source Green's function in frequency domain is chosen as the integral kernel in this study and hybrid source-and-dipole distribution ...In the framework of 3D potential flow theory, Bessho form translating-pulsating source Green's function in frequency domain is chosen as the integral kernel in this study and hybrid source-and-dipole distribution model of the boundary element method is applied to directly solve the velocity potential for advancing ship in regular waves. Numerical characteristics of the Green function show that the contribution of local-flow components to velocity potential is concentrated at the nearby source point area and the wave component dominates the magnitude of velocity potential in the far field. Two kinds of mathematical models, with or without local-flow components taken into account, are adopted to numerically calculate the longitudinal motions of Wigley hulls, which demonstrates the applicability of translating-pulsating source Green's function method for various ship forms. In addition, the mesh analysis of discrete surface is carried out from the perspective of ship-form characteristics. The study shows that the longitudinal motion results by the simplified model are somewhat greater than the experimental data in the resonant zone, and the model can be used as an effective tool to predict ship seakeeping properties. However, translating-pulsating source Green function method is only appropriate for the qualitative analysis of motion response in waves if the ship geometrical shape fails to satisfy the slender-body assumption.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 50879090)
文摘The singularities, oscillatory performances and the contributing factors to the 3-＇D translating-pulsating source Green function of deep-water Havelock form which consists of a local disturbance part and a far-field wave-like part, are analyzed systematically. Relative numerical integral methods about the two parts are presented in this paper. An improved method based on LOBATTO rule is used to eliminate singularities caused respectively by infinite discontinuity and jump discontinuous node from the local disturbance part function, which makes the improvement of calculation efficiency and accuracy possible. And variable substitution is applied to remove the singularity existing at the end of the integral interval of the far-field wave-like part function. Two auxiliary techniques such as valid interval calculation and local refinement of integral steps technique in narrow zones near false singularities are applied so as to avoid unnecessary integration of invalid interval and improve integral accordance. Numerical test results have proved the efficiency and accuracy in these integral methods that thus can be applied to calculate hydrodynamic performance of floating structures moving in waves.
文摘Based on the second order hydroelasticity theory of ships, the numerical methods and the calculated results of the non-linear hydroelastic responses of a ship traveling in rough seas were investigated. The non-linear hydrodynamic actions induced by the rigid body rotations and the variations of instantaneous wetted surface area were included in the second order analysis. The first order wave potentials and responses, which are sure to make the major contributions to the second order hydrodynamic actions, were obtained by employing the translating and pulsating source Green function and the Kelvin steady wave flow solution based on the linear three-dimensional hydroelasticity theory. The influences of the forward speed and the steady wave flow on the responses, and the differences of the predicted non-linear responses were illustrated by the numerical examples of a SWATH ship traveling with forward speed of 12 kn in irregular waves.
基金Project supported by the National Natural Science Foundation of China （No. 50879090）, and the Key Research Program of Hydrody- namics of China （No. 9140A 14030712JB 11044）
文摘The singularities and oscillatory performance of translating-pulsating source Green＇s function in Bessho form were analyzed. Relative numerical integration methods such as Gaussian quadrature rule, variable substitution method （VSM）, and steepest descent integration method （SDIM） were used to evaluate this type of Green＇s function. For SDIM, the complex domain was restricted only on the 0-plane. Meanwhile, the integral along the real axis was computed by use of the VSM to avoid the complication of a numerical search of the steepest descent line. Furthermore, the steepest descent line was represented by the B-spline function. Based on this representation, a new self-compatible integration method corresponding to parametric t was established. The numerical method was validated through comparison with other existing results, and was shown to be efficient and reliable in the calculation of the velocity potentials for the 3D seakeeping and hydrodynamic performance of floating struc- tures moving in waves.
基金Project supported by the National Natural Science Foundation of China(Grant No.50879090)the Key Research Program of Hydrodynamics of China(Grant No.9140A14030712JB11044)
文摘Based on the 3-D surface panel method combined with the translating-pulsating source Green function, an approximate approach is developed to solve the hydrodynamic interacting problem of multiple ships advancing parallel in waves. Focus is on improving the calculating efficiency. In this approach, each ship is assumed to be in each other＇s far-field, and the near-field term in this Green function is neglected if the source point falls on one ship and the field point on others. Further, a matching relationship between the far-field waves and the interfered regions, which are defined as the overlapping areas between the mean wetted body surface of one ship and the propagating regions of the waves generated by another ship, is introduced to avoid the unnecessary computation of the relative terms of the Green function, if the field point is not in the overlapping areas. The approach is validated through studying the hydrodynamic terms and the free motions of two or three ships in side-by-side arrangement by comparing the obtained results with the model tests and the predictions of the exact method. The average calculating speed for the present approximate method is about 1.65-1.8 times of that for the exact method for solving the hydrodynamic interaction problem of two ships, and 2.56-2.73 times for that of three ships.
基金financially supported by the National Natural Science Foundation of China (Grant No. 50879090)Key Research Program of Hydrodynamics of China (Grant No. 9140A14030712JB11044)
文摘A new mathematical integral representation including five integrals about the far field wave shape fimction of Havelock form translating-pulsating source is obtained by performing variable substitution. Constant-phase curves and propagation wave patterns are investigated by applying stationary phase analysis method to the new representation. Some findings are summarized as follows： （1） when 0〈r 〈0.25 （where r is the Strouhal number）, three types of stationary phase curves corresponding to three propagation wave patterns such as fan wave pattern, inner V and outer V wave patterns, are found in the integral representation. （2） When r 〉0.25, besides three types of wave patterns such as a ring-faning wave pattern, a fan wave pattern and an inner V wave pattern, a new one called parallel wave pattern is also found which not only exists in the integrals about the ring-fan wave and fan wave, but also in the integrals whose interval is [0, 7＇] ~ In addition, Characteristics about these parallel waves such as mathematical expressions, existence conditions, propagation directions and wave lengths are obtained, and cancellation relationships between these parallel waves are stated, which certificates the fact that there are no parallel waves existing in the far field.
基金financial support from the National Natural Science Foundation of China under Grant No. 50879090the Key Program of Hydrodynamics of China under Grant No.9140A14030712JB11044
文摘In order to interpret the physical feature of Bessho form translating-pulsating source Green function, the phase function is extracted from the integral representation and stationary-phase analysis is carried out in this paper. The complex characteristics of the integral variable and segmentation of the integral intervals are discussed in m complex plane. In θ space, the interval [-π/2+φ,-π/2+φ-iε] is dominant in the near-field flow, and there is a one-to-one correspondence between the real intervals in m space and the unsteady wave patterns in far field. If 4τ>1(τ is the Brard number), there are three kinds of propagation wave patterns such as ring-fan wave pattern, fan wave pattern and inner V wave pattern, and if 0<4τ<1, a ring wave pattern, an outer V and inner V wave pattern are presented in far field. The ring-fan or ring wave pattern corresponds to the interval [-π+α,-π/2+φ] for integral terms about k2, and the fan or outer V wave pattern and inner V wave pattern correspond to [-π+α,-π/2) and(-π/2,-π/2+φ] respectively for terms about k1. Numerical result shows that it is beneficial to decompose the unsteady wave patterns under the condition of τ≠0 by converting the integral variable θ to m. In addition, the constant-phase curve equations are derived when the source is performing only pulsating or translating.
基金Supported by the National Natural Science Foundation of China(No.51709267 and No.61702531)the National Key Research and Development Project of China(No.2016YFC1401800)the Scientific Research Project of NUDT(ZK16-03-46 and ZK17-03-31)~~
基金financial support from the National Natural Science Foundation of China under Grant No. 50879090the Key Program of Hydrodynamics of China under Grant No. 9140A14030712JB11044+1 种基金Aerospace Support Technology Fund of China (2014)the Postgraduate Innovation Scholarship in Naval University of Engineering
文摘In the framework of 3D potential flow theory, Bessho form translating-pulsating source Green's function in frequency domain is chosen as the integral kernel in this study and hybrid source-and-dipole distribution model of the boundary element method is applied to directly solve the velocity potential for advancing ship in regular waves. Numerical characteristics of the Green function show that the contribution of local-flow components to velocity potential is concentrated at the nearby source point area and the wave component dominates the magnitude of velocity potential in the far field. Two kinds of mathematical models, with or without local-flow components taken into account, are adopted to numerically calculate the longitudinal motions of Wigley hulls, which demonstrates the applicability of translating-pulsating source Green's function method for various ship forms. In addition, the mesh analysis of discrete surface is carried out from the perspective of ship-form characteristics. The study shows that the longitudinal motion results by the simplified model are somewhat greater than the experimental data in the resonant zone, and the model can be used as an effective tool to predict ship seakeeping properties. However, translating-pulsating source Green function method is only appropriate for the qualitative analysis of motion response in waves if the ship geometrical shape fails to satisfy the slender-body assumption.
