To study wave-current actions on 3-D bodies a time-domain numerical model was established using a higher-order boundary element method(HOBEM).By assuming small flow velocities,the velocity potential could be expressed...To study wave-current actions on 3-D bodies a time-domain numerical model was established using a higher-order boundary element method(HOBEM).By assuming small flow velocities,the velocity potential could be expressed for linear and higher order components by perturbation expansion.A 4th-order Runge-Kutta method was applied for time marching.An artificial damping layer was adopted at the outer zone of the free surface mesh to dissipate scattering waves.Validation of the numerical method was carried out on run-up,wave exciting forces,and mean drift forces for wave-currents acting on a bottom-mounted vertical cylinder.The results were in close agreement with the results of a frequency-domain method and a published time-domain method.The model was then applied to compute wave-current forces and run-up on a Seastar mini tension-leg platform.展开更多
The wave diffraction and radiation around a floating body is considered within the framework of the linear potential theory in a fairly perfect fluid. The fluid domain extended infinitely in the horizontal directions ...The wave diffraction and radiation around a floating body is considered within the framework of the linear potential theory in a fairly perfect fluid. The fluid domain extended infinitely in the horizontal directions but is limited by the sea bed, the body hull, and the part of the free surface excluding the body waterplane, and is subdivided into two subdomains according to the body geometry. The two subdomains are connected by a control surface in fluid. In each subdomain, the velocity potential is described by using the usual boundary integral representation involving Green functions. The boundary integral equations are then established by satisfying the boundary conditions and the continuous condition of the potential and the normal derivation across the control surface. This multi-domain boundary element method (MDBEM) is particularly interesting for bodies with a hull form including moonpools to which the usual BEM presents singularities and slow convergence of numerical results. The application of the MDBEM to study the resonant motion of a water column in moonpools shows that the MDBEM provides an efficient and reliable prediction method.展开更多
The simulations of nonlinear sloshing in both two-dimensional and three-dimensional liquid tanks with porosity girder are carried out in time domain by using the Multi-domain Boundary Element Method(MBEM).The compar...The simulations of nonlinear sloshing in both two-dimensional and three-dimensional liquid tanks with porosity girder are carried out in time domain by using the Multi-domain Boundary Element Method(MBEM).The comparison of the present results and the references is conducted and shows they agree well with each other.The three-dimensional effect and the influence of the width of liquid tank and the height and porosity of the girder on the natural period of the model are also discussed.展开更多
Through a higher-order boundary element method based on NURBS (Non-uniform Rational B-splines), the calculation of second-order low-frequency forces and slow drift motions is conducted for floating bodies. In the fl...Through a higher-order boundary element method based on NURBS (Non-uniform Rational B-splines), the calculation of second-order low-frequency forces and slow drift motions is conducted for floating bodies. In the floating body's inner domain, an auxiliary equation is obtained by applying a Green function which satisfies the solid surface condition. Then, the auxiliary equation and the velocity potential equation are combined in the fluid domain to remove the solid angle coefficient and the singularity of the double layer potentials in the integral equation. Thus, a new velocity potential integral equation is obtained. The new equation is extended to the inner domain to reheve the irregular frequency effects; on the basis of the order analysis, the comparison is made about the contribution of all integral terms with the result in the second-order tow-frequency problem; the higher-order boundary element method based on NURBS is apphed to calculate the geometric position and velocity potentials; the slow drift motions are calculated by the spectrum analysis method. Removing the solid angle coefficient can apply NURBS technology to the hydrodynamic calculation of floating bodies with complex surfaces, and the extended boundary integral method can reduce the irregular frequency effects. Order analysis shows that free surface integral can be neglected, and the numerical results can also prove the correctness of order analysis. The results of second-order low-frequency forces and slow drift motions and the comparison with the results from references show that the application of the NURBS technology to the second-order low-frequency problem is of high efficiency and credible results.展开更多
A 3-D time-domain seakeeping analysis tool has been newly developed by using a higher-order boundary element method with the Rankine source as the kernel function. An iterative time-marching scheme for updating both k...A 3-D time-domain seakeeping analysis tool has been newly developed by using a higher-order boundary element method with the Rankine source as the kernel function. An iterative time-marching scheme for updating both kinematic and dynamic free-surface boundary conditions is adopted for achieving numerical accuracy and stability. A rectangular computational domain moving with the mean speed of ship is introduced. A damping beach at the outer portion of the truncated free surface is installed for satisfying the radiation condition. After numerical convergence checked, the diffraction unsteady problem of a Wigley hull traveling with a constant forward speed in waves is studied. Extensive results including wave exciting forces, wave patterns and pressure distributions on the hull are presented to validate the efficiency and accuracy of the proposed 3-D time-domain iterative Rankine BEM approach. Computed results are compared to be in good agreement with the corresponding experimental data and other published numerical solutions.展开更多
Based on the time-domain higher-order boundary element method(HOBEM), a two-dimensional numerical wave flume is developed to investigate solitary wave interaction with two rectangular boxes with a narrow gap.In the nu...Based on the time-domain higher-order boundary element method(HOBEM), a two-dimensional numerical wave flume is developed to investigate solitary wave interaction with two rectangular boxes with a narrow gap.In the numerical model, the fully nonlinear boundary conditions are satisfied on the free surface, the mixed Eulerian-Lagrangian method is adopted to track the transient water surface and the fourth-order Runga-Kutta method is used to predict the velocity potential and wave elevation on the free surface. The acceleration potential technique is used to compute the transient wave forces along the wetted object surface. A piston-type wavemaker is used to generate solitary waves. The proposed model is validated by comparing the simulated wave run-up and the wave loads with the published experimental and numerical results of the reflection of a solitary wave from a vertical wall. Then, numerical experiments are performed to study the effects of the narrow gap and the size of each box on the wave run-ups at the two sides of the two-box system and in the narrow gap between two boxes, and the wave loads on the two boxes. The interaction between double solitary waves with a time interval between them with a two-box system is also investigated.展开更多
An integral equation approach is utilized to in- vestigate the added mass and damping of floating produc- tion, storage and offloading system (FPSO system). Finite water depth Green function and higher-order boundar...An integral equation approach is utilized to in- vestigate the added mass and damping of floating produc- tion, storage and offloading system (FPSO system). Finite water depth Green function and higher-order boundary ele- ment method are used to solve integral equation. Numeri- cal results about added mass and damping are presented for odd and even mode motions of FPSO. The results show ro- bust convergence in high frequency range and can be used in wave load analysis for FPSO designing and operation.展开更多
A fully nonlinear numerical model based on a time-domain higher-order boundary element method (HOBEM) is founded to simulate the kinematics of extreme waves. In the model, the fully nonlinear free surface boundary c...A fully nonlinear numerical model based on a time-domain higher-order boundary element method (HOBEM) is founded to simulate the kinematics of extreme waves. In the model, the fully nonlinear free surface boundary conditions are satisfied and a semi-mixed Euler-Lagrange method is used to track free surface; a fourth-order Runga-Kutta technique is adopted to refresh the wave elevation and velocity potential on the free surface at each time step; an image Green function is used in the numerical wave tank so that the integrations on the lateral surfaces and bottom are excluded. The extreme waves are generated by the method of wave focusing. The physical experiments are carried out in a wave flume. On the horizontal velocity of the measured point, numerical solutions agree well with experimental results. The characteristics of the nonlinear extreme-wave kinematics and the velocity distribution are studied here.展开更多
A numerical model is developed to simulate fully nonlinear extreme waves in finite and infinite water-depth wave tanks. A semi-mixed Enlerian-Lagrangian formulation is adopted and a higher-order boundary element metho...A numerical model is developed to simulate fully nonlinear extreme waves in finite and infinite water-depth wave tanks. A semi-mixed Enlerian-Lagrangian formulation is adopted and a higher-order boundary element method in conjunction with an image Green function is used for the fluid domain. The botmdary values on the free surface are updated at each time step by a fourth-order Runga-Kutta time-marching scheme at each time step. Input wave characteristics are specified at the upstream boundary by an appropriate wave theory. At the downstream boundary, an artificial damping zone is used to prevent wave reflection back into the computational domain. Using the image Green function in the whole fluid domain, the integrations on the two lateral walls and bottom are excluded. The simulation results on extreme wave elevations in finite and infinite water-depths are compared with experimental results and second-order analytical solutions respectively. The wave kinematics is also discussed in the present study.展开更多
Coastal wave energy resources have enormous exploitation potential due to shorter weather window,closer installation distance and lower maintenance cost.However,impact loads generated by depth variation from offshore ...Coastal wave energy resources have enormous exploitation potential due to shorter weather window,closer installation distance and lower maintenance cost.However,impact loads generated by depth variation from offshore to nearshore and wave-current interaction,may lead to a catastrophic damage or complete destruction to wave energy converters(WECs).This objective of this paper is to investigate slamming response of a coastal oscillating wave surge converter(OWSC)entering or leaving water freely.Based on fully nonlinear potential flow theory,a time-domain wave-current-structure interaction model combined with higher-order boundary element method(HOBEM),is developed to analyze the coupled hydrodynamic problem.The variable-depth seabed is considered in the model to illustrate the shallow water effect on impact loads and free surface profiles in coastal zone.A domain decomposition approach is utilized to simulate the overlapping phenomenon generated by a jet falling into water under gravity effect.Through a series of Lagrangian interpolation methods,the meshes on boundaries are rearranged to avoid the mismatch between element size on free surface and body surface.The present model is validated against the existing experimental and numerical results.Simulations are also provided for the effects of wave-current interaction and uneven local seabed on the slamming responses.It is found that the length of the splash jet increases for a following current and decreases for an opposing current,and that the slamming response of the OWSC device is sensitive to the geometric features of the uneven seabed.展开更多
A Time-domain Higher-Order Boundary Element Method(THOBEM) is developed for simulating wave-current interactions with 3-D floating bodies.Through a Taylor series expansion and a perturbation procedure,the model is f...A Time-domain Higher-Order Boundary Element Method(THOBEM) is developed for simulating wave-current interactions with 3-D floating bodies.Through a Taylor series expansion and a perturbation procedure,the model is formulated to the first-order in the wave steepness and in the current velocity,respectively.The boundary value problem is decomposed into a steady double-body flow problem and an unsteady wave problem.Higher-order boundary integral equation methods are then used to solve the proposed problems with a fourth-order Runge-Kutta method for the time marching.An artificial damping layer is adopted to dissipate the scattering waves.Different from the other time-domain numerical models,which are often focused on the wave-current interaction with restrained bodies,the present model deals with a floating hemisphere.The numerical results of wave forces,wave run-up and body response are all in a close agreement with those obtained by frequency-domain methods.The proposed numerical model is further applied to investigate wave-current interactions with a floating body of complicated geometry.In this work,the regular and focused wave combined with current interacting with a truss-spar platform is investigated.展开更多
A time-domain numerical algorithm based on the higher-order boundary element method and the iterative time-marching scheme is proposed for seakeeping analysis. The ship waves generated by a hull advancing at a constan...A time-domain numerical algorithm based on the higher-order boundary element method and the iterative time-marching scheme is proposed for seakeeping analysis. The ship waves generated by a hull advancing at a constant forward speed in incident waves and the resultant diffraction forces acting on the hull are computed to investigate the hull-form effects on the hydrodynamic forces. A rectangular computational domain travelling at ship's speed is considered. An artificial damping beach for satisfying the radiation condition is installed at the outer portion of the free surface except the downstream side. An iterative time-marching scheme is employed for updating both kinematic and dynamic free-surface boundary conditions for numerical accuracy and stability. The boundary integral equation is solved by distributing higher-order boundary elements over the wetted body surface and the free surface. The hull-form effects on the naval hydrodynamics are investigated by comparing three different Wigley models. Finally, the corresponding unsteady wave patterns and the wave profiles around the hulls are illustrated and discussed.展开更多
The body-fixed coordinate system is applied to the wave-body interaction problem of a small-depth elastic structure which has both rigid and elastic body motions in head waves.In the weakly non-linear assumption,the p...The body-fixed coordinate system is applied to the wave-body interaction problem of a small-depth elastic structure which has both rigid and elastic body motions in head waves.In the weakly non-linear assumption,the perturbation scheme is used and the expansion is conducted up to second-order to consider several non-linear quantities.To solve the boundary value problem,linearization is carried out based not on inertial coordinate but on body-fixed coordinate which could be accelerated by a motion of a body.At first,the main feature of the application of body-fixed coordinate system for a seakeeping problem is briefly described.After that the transformation of a coordinate system is extended to consider an elastic body motion and several physical variables are re-described in the generalized mode.It has been found that the deformation gradient could be used for the transformation of a coordinate system if several conditions are satisfied.Provided there are only vertical bending in elastic modes and the structure has relatively small depth,these conditions are generally satisfied.To calculate an elastic motion of a body,the generalized mode method is adopted and the mode shape is obtained by solving eigen-value problem of dynamic beam equation.In the boundary condition of the body-fixed coordinate system,the motion effect reflected to free-surface boundary is considered by extrapolating each mode shape to the horizontal direction from a body.At last,simple numerical tests are implemented as a validation process.The second-order hydrodynamic force of a freely floating hemisphere is first calculated in zero forward speed condition.Next,motion and added resistance of a ship with forward speed are considered at different flexibility to confirm the effect of an elastic body motion in body-fixed coordinate system.展开更多
基金Supported by the National Natural Science Foundation of China under (Grant No.107 72040,50709005 and 50921001)the Major National Science and Technology Projects of China under (Grant No.2008ZX05026-02)the Open Fund of State Key Laboratory of Ocean Engineering
文摘To study wave-current actions on 3-D bodies a time-domain numerical model was established using a higher-order boundary element method(HOBEM).By assuming small flow velocities,the velocity potential could be expressed for linear and higher order components by perturbation expansion.A 4th-order Runge-Kutta method was applied for time marching.An artificial damping layer was adopted at the outer zone of the free surface mesh to dissipate scattering waves.Validation of the numerical method was carried out on run-up,wave exciting forces,and mean drift forces for wave-currents acting on a bottom-mounted vertical cylinder.The results were in close agreement with the results of a frequency-domain method and a published time-domain method.The model was then applied to compute wave-current forces and run-up on a Seastar mini tension-leg platform.
文摘The wave diffraction and radiation around a floating body is considered within the framework of the linear potential theory in a fairly perfect fluid. The fluid domain extended infinitely in the horizontal directions but is limited by the sea bed, the body hull, and the part of the free surface excluding the body waterplane, and is subdivided into two subdomains according to the body geometry. The two subdomains are connected by a control surface in fluid. In each subdomain, the velocity potential is described by using the usual boundary integral representation involving Green functions. The boundary integral equations are then established by satisfying the boundary conditions and the continuous condition of the potential and the normal derivation across the control surface. This multi-domain boundary element method (MDBEM) is particularly interesting for bodies with a hull form including moonpools to which the usual BEM presents singularities and slow convergence of numerical results. The application of the MDBEM to study the resonant motion of a water column in moonpools shows that the MDBEM provides an efficient and reliable prediction method.
基金supported by the National Natural Science Foundation of China (Grant No. 50639020)the National High Technology Research and Development Program of China (863 Program, Grant No. 2006AA332Z09)the Fund in State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University (Grant No. GKZD010012)
文摘The simulations of nonlinear sloshing in both two-dimensional and three-dimensional liquid tanks with porosity girder are carried out in time domain by using the Multi-domain Boundary Element Method(MBEM).The comparison of the present results and the references is conducted and shows they agree well with each other.The three-dimensional effect and the influence of the width of liquid tank and the height and porosity of the girder on the natural period of the model are also discussed.
文摘Through a higher-order boundary element method based on NURBS (Non-uniform Rational B-splines), the calculation of second-order low-frequency forces and slow drift motions is conducted for floating bodies. In the floating body's inner domain, an auxiliary equation is obtained by applying a Green function which satisfies the solid surface condition. Then, the auxiliary equation and the velocity potential equation are combined in the fluid domain to remove the solid angle coefficient and the singularity of the double layer potentials in the integral equation. Thus, a new velocity potential integral equation is obtained. The new equation is extended to the inner domain to reheve the irregular frequency effects; on the basis of the order analysis, the comparison is made about the contribution of all integral terms with the result in the second-order tow-frequency problem; the higher-order boundary element method based on NURBS is apphed to calculate the geometric position and velocity potentials; the slow drift motions are calculated by the spectrum analysis method. Removing the solid angle coefficient can apply NURBS technology to the hydrodynamic calculation of floating bodies with complex surfaces, and the extended boundary integral method can reduce the irregular frequency effects. Order analysis shows that free surface integral can be neglected, and the numerical results can also prove the correctness of order analysis. The results of second-order low-frequency forces and slow drift motions and the comparison with the results from references show that the application of the NURBS technology to the second-order low-frequency problem is of high efficiency and credible results.
基金supported by the Fundamental Research Developing Association for Shipbuilding and Offshore (REDAS), Japan
文摘A 3-D time-domain seakeeping analysis tool has been newly developed by using a higher-order boundary element method with the Rankine source as the kernel function. An iterative time-marching scheme for updating both kinematic and dynamic free-surface boundary conditions is adopted for achieving numerical accuracy and stability. A rectangular computational domain moving with the mean speed of ship is introduced. A damping beach at the outer portion of the truncated free surface is installed for satisfying the radiation condition. After numerical convergence checked, the diffraction unsteady problem of a Wigley hull traveling with a constant forward speed in waves is studied. Extensive results including wave exciting forces, wave patterns and pressure distributions on the hull are presented to validate the efficiency and accuracy of the proposed 3-D time-domain iterative Rankine BEM approach. Computed results are compared to be in good agreement with the corresponding experimental data and other published numerical solutions.
基金The National Natural Science Foundation of China under contract Nos 51679036,51222902 and 51490672the Program for New Century Excellent Talents in University under contract No.NCET-13-0076
文摘Based on the time-domain higher-order boundary element method(HOBEM), a two-dimensional numerical wave flume is developed to investigate solitary wave interaction with two rectangular boxes with a narrow gap.In the numerical model, the fully nonlinear boundary conditions are satisfied on the free surface, the mixed Eulerian-Lagrangian method is adopted to track the transient water surface and the fourth-order Runga-Kutta method is used to predict the velocity potential and wave elevation on the free surface. The acceleration potential technique is used to compute the transient wave forces along the wetted object surface. A piston-type wavemaker is used to generate solitary waves. The proposed model is validated by comparing the simulated wave run-up and the wave loads with the published experimental and numerical results of the reflection of a solitary wave from a vertical wall. Then, numerical experiments are performed to study the effects of the narrow gap and the size of each box on the wave run-ups at the two sides of the two-box system and in the narrow gap between two boxes, and the wave loads on the two boxes. The interaction between double solitary waves with a time interval between them with a two-box system is also investigated.
基金supported by the Fundamental Research Funds forthe Central Universities (DVT10LK43)the Returned Overseas Chinese Scholars,State Education Ministry (2007[24])
文摘An integral equation approach is utilized to in- vestigate the added mass and damping of floating produc- tion, storage and offloading system (FPSO system). Finite water depth Green function and higher-order boundary ele- ment method are used to solve integral equation. Numeri- cal results about added mass and damping are presented for odd and even mode motions of FPSO. The results show ro- bust convergence in high frequency range and can be used in wave load analysis for FPSO designing and operation.
基金The National Natural Science Foundations of China under contract Nos 50709005 and 50639030the Program for Changjiang Scholars and Innovative Research Teams of Universities and Colleges of China under contract No. IRT0420the National High Tech Research and Development Program of China under contract No.2006AA09A109-3
文摘A fully nonlinear numerical model based on a time-domain higher-order boundary element method (HOBEM) is founded to simulate the kinematics of extreme waves. In the model, the fully nonlinear free surface boundary conditions are satisfied and a semi-mixed Euler-Lagrange method is used to track free surface; a fourth-order Runga-Kutta technique is adopted to refresh the wave elevation and velocity potential on the free surface at each time step; an image Green function is used in the numerical wave tank so that the integrations on the lateral surfaces and bottom are excluded. The extreme waves are generated by the method of wave focusing. The physical experiments are carried out in a wave flume. On the horizontal velocity of the measured point, numerical solutions agree well with experimental results. The characteristics of the nonlinear extreme-wave kinematics and the velocity distribution are studied here.
基金supported by the National Natural Science Foundation of China (Grant Nos .50709005 ,50639030 and 10772040)the National High Technology Research and Development Program of China (Grant No.2006AA09A109-3) UK EPSRC(Grant Nos . GR/T07220/01 and GR/T07220/02)
文摘A numerical model is developed to simulate fully nonlinear extreme waves in finite and infinite water-depth wave tanks. A semi-mixed Enlerian-Lagrangian formulation is adopted and a higher-order boundary element method in conjunction with an image Green function is used for the fluid domain. The botmdary values on the free surface are updated at each time step by a fourth-order Runga-Kutta time-marching scheme at each time step. Input wave characteristics are specified at the upstream boundary by an appropriate wave theory. At the downstream boundary, an artificial damping zone is used to prevent wave reflection back into the computational domain. Using the image Green function in the whole fluid domain, the integrations on the two lateral walls and bottom are excluded. The simulation results on extreme wave elevations in finite and infinite water-depths are compared with experimental results and second-order analytical solutions respectively. The wave kinematics is also discussed in the present study.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.52025112 and 51861130358)the State Key Laboratory of Ocean Engineering+1 种基金China(Shanghai Jiao Tong University)(Grant No.1905)the Newton Advanced Fellowships(Grant No.NAF\R1\180304)by the Royal Society。
文摘Coastal wave energy resources have enormous exploitation potential due to shorter weather window,closer installation distance and lower maintenance cost.However,impact loads generated by depth variation from offshore to nearshore and wave-current interaction,may lead to a catastrophic damage or complete destruction to wave energy converters(WECs).This objective of this paper is to investigate slamming response of a coastal oscillating wave surge converter(OWSC)entering or leaving water freely.Based on fully nonlinear potential flow theory,a time-domain wave-current-structure interaction model combined with higher-order boundary element method(HOBEM),is developed to analyze the coupled hydrodynamic problem.The variable-depth seabed is considered in the model to illustrate the shallow water effect on impact loads and free surface profiles in coastal zone.A domain decomposition approach is utilized to simulate the overlapping phenomenon generated by a jet falling into water under gravity effect.Through a series of Lagrangian interpolation methods,the meshes on boundaries are rearranged to avoid the mismatch between element size on free surface and body surface.The present model is validated against the existing experimental and numerical results.Simulations are also provided for the effects of wave-current interaction and uneven local seabed on the slamming responses.It is found that the length of the splash jet increases for a following current and decreases for an opposing current,and that the slamming response of the OWSC device is sensitive to the geometric features of the uneven seabed.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10772040, 50709005 and 5092100)the Important National Science and Technology Specific Projects of China (Grant No. 2008ZX05026-02)the Open Fund of Stabe Key Laboratory of Sabllite Ocean Environment Dynamics (Grant No. SOED1002)
文摘A Time-domain Higher-Order Boundary Element Method(THOBEM) is developed for simulating wave-current interactions with 3-D floating bodies.Through a Taylor series expansion and a perturbation procedure,the model is formulated to the first-order in the wave steepness and in the current velocity,respectively.The boundary value problem is decomposed into a steady double-body flow problem and an unsteady wave problem.Higher-order boundary integral equation methods are then used to solve the proposed problems with a fourth-order Runge-Kutta method for the time marching.An artificial damping layer is adopted to dissipate the scattering waves.Different from the other time-domain numerical models,which are often focused on the wave-current interaction with restrained bodies,the present model deals with a floating hemisphere.The numerical results of wave forces,wave run-up and body response are all in a close agreement with those obtained by frequency-domain methods.The proposed numerical model is further applied to investigate wave-current interactions with a floating body of complicated geometry.In this work,the regular and focused wave combined with current interacting with a truss-spar platform is investigated.
基金Project supported by the National Natural Science Foun-dation of China(Grant Nos.51579058,11502059)the Shandong Provincial Natural Science Foundation(Grant No.ZR2014EEQ016)
文摘A time-domain numerical algorithm based on the higher-order boundary element method and the iterative time-marching scheme is proposed for seakeeping analysis. The ship waves generated by a hull advancing at a constant forward speed in incident waves and the resultant diffraction forces acting on the hull are computed to investigate the hull-form effects on the hydrodynamic forces. A rectangular computational domain travelling at ship's speed is considered. An artificial damping beach for satisfying the radiation condition is installed at the outer portion of the free surface except the downstream side. An iterative time-marching scheme is employed for updating both kinematic and dynamic free-surface boundary conditions for numerical accuracy and stability. The boundary integral equation is solved by distributing higher-order boundary elements over the wetted body surface and the free surface. The hull-form effects on the naval hydrodynamics are investigated by comparing three different Wigley models. Finally, the corresponding unsteady wave patterns and the wave profiles around the hulls are illustrated and discussed.
文摘The body-fixed coordinate system is applied to the wave-body interaction problem of a small-depth elastic structure which has both rigid and elastic body motions in head waves.In the weakly non-linear assumption,the perturbation scheme is used and the expansion is conducted up to second-order to consider several non-linear quantities.To solve the boundary value problem,linearization is carried out based not on inertial coordinate but on body-fixed coordinate which could be accelerated by a motion of a body.At first,the main feature of the application of body-fixed coordinate system for a seakeeping problem is briefly described.After that the transformation of a coordinate system is extended to consider an elastic body motion and several physical variables are re-described in the generalized mode.It has been found that the deformation gradient could be used for the transformation of a coordinate system if several conditions are satisfied.Provided there are only vertical bending in elastic modes and the structure has relatively small depth,these conditions are generally satisfied.To calculate an elastic motion of a body,the generalized mode method is adopted and the mode shape is obtained by solving eigen-value problem of dynamic beam equation.In the boundary condition of the body-fixed coordinate system,the motion effect reflected to free-surface boundary is considered by extrapolating each mode shape to the horizontal direction from a body.At last,simple numerical tests are implemented as a validation process.The second-order hydrodynamic force of a freely floating hemisphere is first calculated in zero forward speed condition.Next,motion and added resistance of a ship with forward speed are considered at different flexibility to confirm the effect of an elastic body motion in body-fixed coordinate system.