This paper presents a study on the motion response of a tension-leg platform(TLP) under first-and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave fo...This paper presents a study on the motion response of a tension-leg platform(TLP) under first-and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave force is calculated using the full-field quadratic transfer function(QTF). The coupled effect of the horizontal motions, such as surge, sway and yaw motions, and the set-down motion are taken into consideration by the nonlinear restoring matrix. The time-domain analysis with 50-yr random sea state is performed. A comparison of the results of different case studies is made to assess the influence of second-order wave force on the motions of the platform. The analysis shows that the second-order wave force has a major impact on motions of the TLP. The second-order difference-frequency wave force has an obvious influence on the low-frequency motions of surge and sway, and also will induce a large set-down motion which is an important part of heave motion. Besides, the second-order sum-frequency force will induce a set of high-frequency motions of roll and pitch. However, little influence of second-order wave force is found on the yaw motion.展开更多
The selection of wave force models will significantly impact the structural responses of floating wind turbines.In this study,comparisons of wave force model effects on the structural responses and fatigue loads of a ...The selection of wave force models will significantly impact the structural responses of floating wind turbines.In this study,comparisons of wave force model effects on the structural responses and fatigue loads of a semi-submersible floating wind turbine(SFWT)were conducted.Simulations were performed by employing the Morison equation(ME)with linear or second-order wave kinematics and potential flow theory(PFT)with first-or second-order wave forces.A comparison of regular waves,irregular waves,and coupled wind/waves analyses with the experimental data showed that many of the simulation results and experimental data are relatively consistent.However,notable discrepancies are found in the response amplitude operators for platform heave,tower base bending moment,and tension in mooring lines.PFT models give more satisfactory results of heave but more significant discrepan-cies in tower base bending moment than the ME models.In irregular wave analyses,low-frequency resonances were captured by PFT models with second-order difference-frequency terms,and high-frequency resonances were captured by the ME models or PFT models with second-order sum-frequency terms.These force models capture the response frequencies but do not reasonably predict the response amplitudes.The coupled wind/waves analyses showed more satisfactory results than the wave-only analyses.However,an important detail to note is that this satisfactory result is based on the overprediction of wind-induced responses.展开更多
-In this paper, an analytical solution in the outer region of finite water depth is derived for the second-order diffraction potential, which gives a clear physical meaning of the wave transmission and reflection char...-In this paper, an analytical solution in the outer region of finite water depth is derived for the second-order diffraction potential, which gives a clear physical meaning of the wave transmission and reflection characteristics in the far field. A numerical method-simple Green's function technique-for calculating the second-order diffraction potential in the inner region is also described. Numerical results are provided for the second-order wave forces on a semi-submerged cylinder. It is found that the contribution of second-order diffraction potential to second-order wave forces is important. The effect of water depth and submerged depth on the wave force is also discussed.展开更多
A numerical study based on a two-dimensional two-phase SPH(Smoothed Particle Hydrodynamics)model to analyze the action of water waves on open-type sea access roads is presented.The study is a continuation of the analy...A numerical study based on a two-dimensional two-phase SPH(Smoothed Particle Hydrodynamics)model to analyze the action of water waves on open-type sea access roads is presented.The study is a continuation of the analyses presented by Chen et al.(2022),in which the sea access roads are semi-immersed.In this new configuration,the sea access roads are placed above the still water level,therefore the presence of the air phase becomes a relevant issue in the determination of the wave forces acting on the structures.Indeed,the comparison of wave forces on the open-type sea access roads obtained from the single and two-phase SPH models with the experimental results shows that the latter are in much better agreement.So in the numerical simulations,a two-phaseδ-SPH model is adopted to investigate the dynamical problems.Based on the numerical results,the maximum horizontal and uplifting wave forces acting on the sea access roads are analyzed by considering different wave conditions and geometries of the structures.In particular,the presence of the girder is analyzed and the differences in the wave forces due to the air cushion effects which are created below the structure are highlighted.展开更多
In this paper, we will concern the existence, asymptotic behaviors and stability of forced pulsating waves for a Lotka-Volterra cooperative system with nonlocal effects under shifting habitats. By using the alternativ...In this paper, we will concern the existence, asymptotic behaviors and stability of forced pulsating waves for a Lotka-Volterra cooperative system with nonlocal effects under shifting habitats. By using the alternatively-coupling upper-lower solution method, we establish the existence of forced pulsating waves, as long as the shifting speed falls in a finite interval where the endpoints are obtained from KPP-Fisher speeds. The asymptotic behaviors of the forced pulsating waves are derived. Finally, with proper initial, the stability of the forced pulsating waves is studied by the squeezing technique based on the comparison principle.展开更多
The second-order effect of axial force on horizontal vibrating characteristics of a large-diameter pipe pile is theoretically investigated.Governing equations of the pile-soil system are established based on elastodyn...The second-order effect of axial force on horizontal vibrating characteristics of a large-diameter pipe pile is theoretically investigated.Governing equations of the pile-soil system are established based on elastodynamics.Threedimensional wave equations of soil are decoupled through differential transformation and variable separation.Consequently,expressions of soil displacements and horizontal resistances can be obtained.An analytical solution of the pile is derived based on continuity conditions between the pile and soil,subsequently from which expressions of the complex impedances are deduced.Analyses are carried out to examine the second-order effect of axial force on the horizontal vibrating behavior of the pipe pile.Some conclusions can be summarized as follows： stiffness and damping factors are decreased with the application of axial force on the pile head; distributions of the pile horizontal displacement and rotation angle are regenerated due to the second-order effect of the applied axial force; and redistributions of the bending moment and shearing force occur due to the second-order effect of the applied axial force.展开更多
Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for ...Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.展开更多
A numerical model of wave force upon continuous cylinder structures with a large diameter using the boundary element method (BEM) is presented. A numerical model of reflecting wave upon continuous cylinders was establ...A numerical model of wave force upon continuous cylinder structures with a large diameter using the boundary element method (BEM) is presented. A numerical model of reflecting wave upon continuous cylinders was established on the basis of linear wave theory.The fundamental solution to the Helmholtz equation within an infinite strip area that explicitly satisfies two infinite parallel boundaries is used together with Radiation condition rather than the solution of an infinite area.According to the proposed theory and method,the computer programs have been composed in Visual C ++ Development Studio.Several examples show that the technique and its program are feasible and efficient.And the wave forces upon continuous cylinders can be decreased by as much as 14%～24% under a ratio of D/L= 0.09～0.19 compared with the square caissons.展开更多
The results of design and experiment of a submerged semi-circular breakwater at the Yangtze estuary show that the submerged structure will be unsafe when the general empirical wave force formula for semi-circular brea...The results of design and experiment of a submerged semi-circular breakwater at the Yangtze estuary show that the submerged structure will be unsafe when the general empirical wave force formula for semi-circular breakwater is used in design. Therefore, a new calculation method for the wave forces acting on a submerged semi-circular structure is given in this paper, in which the wave force acting on the inside circumference of semi-circular arch is included, and the phase modification coefficient in the general empirical formula is adjusted as well. The new wave force calculation method has been Verified by the results of seven related physical model tests and adopted in the design of the south esturary jetty of the first stage project of Deep Channel Improvement Project of the Yangtze River Estuary, the total jetty length being 17.5 km.展开更多
Numerical simulations are carried out for wave action on a submerged horizontal circular cylinder by means of a viscous fluid model, and it is focused on the examination of the discrepancies between the viscous fluid ...Numerical simulations are carried out for wave action on a submerged horizontal circular cylinder by means of a viscous fluid model, and it is focused on the examination of the discrepancies between the viscous fluid results and the potential flow solutions. It is found that the lift force resulted from rotational flow on the circular cylinder is always in anti-phase with the inertia force and induces the discrepancies between the results. The influence factors on the magnitude of the lift force, especially the correlation between the stagnation-point position and the wave amplitude, and the effect of the vortex shedding are investigated by further examination on the flow fields around the cylinder. The viscous numerical calculations at different wave frequencies showed that the wave frequency has also significant influence on the wave forces. Under higher frequency and larger amplitude wave action, vortex shedding from the circular cylinder will appear and influence the wave forces on the cylinder substantially.展开更多
Wave forces induced by the interaction between the oblique incident wave and the breakwater with a partially perforated front wall is investigated. The fluid domain is divided into two sub-domains and the eigen-functi...Wave forces induced by the interaction between the oblique incident wave and the breakwater with a partially perforated front wall is investigated. The fluid domain is divided into two sub-domains and the eigen-function expansion method is applied to expanding velocity potentials in each domain. In the eigen-expansion of the velocity potential, evanescent waves are included. Numerical results of the present model are compared with other theories and a good agreement can be found between them. Experimental data have been compared with the present theoretical results. The effect of the traverse wall on wave forces has been discussed in detail. On the basis of the linear wave theory, it is shown that in the range Of engineering practice, the incident angle of wave has small influence on wave forces on the unit length of perforated caisson.展开更多
For the computation of wave forces on structures, a B-spline expansion is applied to discretize the body surface, and represent the velocity potentials on the body surface. The expansion coefficients for the body geom...For the computation of wave forces on structures, a B-spline expansion is applied to discretize the body surface, and represent the velocity potentials on the body surface. The expansion coefficients for the body geometry are determined by the Least Square Method, and the coefficients for velocity potentials by the Galerkin method. The method can give continuous description of velocity potentials and their derivatives on the whole smooth body surface. The method has been implemented, and numerical results show that the method gives very accurate results and its convergence is fast.展开更多
A time-domain method is applied to simulate nonlinear wave diffraction around a surface piercing 3-D arbitrary body. The method involves the application of Taylor series expansions and the use of perturbation procedur...A time-domain method is applied to simulate nonlinear wave diffraction around a surface piercing 3-D arbitrary body. The method involves the application of Taylor series expansions and the use of perturbation procedure to establish the corresponding boundary value problems with respect to a time-independent fluid domain. A boundary element method based on B-spline expansion is used to calculate the wave field at each time step, and the free surface boundary condition is satisfied to the second order of wave steepness by a numerical integration in time. An artificial damping layer is adopted on the free surface for the removal of wave reflection from the outer boundary. As an illustration, the method is used to compute the second-order wave forces and run-up on a surface-piercing circular cylinder. The present method is found to be accurate, computationally efficient, and numerically stable.展开更多
A series of experimental studies about the force of internal solitary wave and internal periodic wave on vertical cylinders have been carried out in a two-dimensional layered internal wave flume. The internal solitary...A series of experimental studies about the force of internal solitary wave and internal periodic wave on vertical cylinders have been carried out in a two-dimensional layered internal wave flume. The internal solitary waves are produced by means of gravitational collapse at the layer thickness ratio of 0.2, and the internal periodic waves are produced with rocker-flap wave maker at the layer thickness ratio of 0.93. The wave parameters are obtained through dyeing photography. The vertical cylinders of the same size are arranged in different depths. The horizontal force on each cylinder is measured and the vertical distribution rules are researched. The internal wave heights are changed to study the impact of wave heights on the force. The results show that the horizontal force of concave type internal solitary wave on vertical cylinder in the upper-layer fluid has the same direction as the wave propagating, while it has an opposite direction in the lower-layer. The horizontal force is not evenly distributed in the lower fluid. And the force at different depths increases along with wave height. Internal solitary wave can produce an impact load on the entire pile. The horizontal force of internal periodic waves on the vertical cylinders is periodically changed at the frequency of waves. The direction of the force is opposite in the upper and lower layers, and the value is close. In the upper layer except the depth close to the interface, the force is evenly distributed; but it tends to decrease with the deeper depth in the lower layer. A periodic shear load can be produced on the entire pile by internal periodic waves, and it may cause fatigue damage to structures.展开更多
The reflection coefficient and the total horizontal forces of regular waves acting on theperforated caisson are experimentally investigated. The empirical relationship between reflection coefficient and the ratio of t...The reflection coefficient and the total horizontal forces of regular waves acting on theperforated caisson are experimentally investigated. The empirical relationship between reflection coefficient and the ratio of the total horizontal forces acting on the perforated caisson to those on solid vertical walls with the relative chamber width, relative water depth and porosity of perforated wall, etc. are given. Moreover, the results of the ratio of the total horizontal forces are also compared with formulas given by Chinese Harbour Design Criteria and Takahashi, which may be useful for the practical engineering application.展开更多
Based on model tests, the lift and resultant forces on small square cylinders caused by waves (regular and irregular) and currents are analyzed in this paper. The lift and resultant force coefficients CL and Cf relate...Based on model tests, the lift and resultant forces on small square cylinders caused by waves (regular and irregular) and currents are analyzed in this paper. The lift and resultant force coefficients CL and Cf related to KC number and the effect of direction of wave propagation are also given, which may be useful for practical engineering application.展开更多
A complete semi-analytical solution is obtained for second-order diffraction of plane bichromatic waves by a fixed truncated circular column.The fluid domain is divided into interior and exterior regions.In the exteri...A complete semi-analytical solution is obtained for second-order diffraction of plane bichromatic waves by a fixed truncated circular column.The fluid domain is divided into interior and exterior regions.In the exterior region,the second-order velocity potential is expressed in terms of‘locked-wave’and‘free-wave’ components,both are solved using Fourier and eigenfunction expansions.The re- sulting‘locked wave’potential is expressed by one-dimensional Green's integrals with oscillating integrands.In order to increase computational efficiency,the far-field part of the integrals are carried out analytically.Solutions in both regions are matched on the interface by the potential and its normal derivative continuity conditions.Based on the present approach,the sum-and difference-frequency potentials are efficiently evaluated and are used to generate the quadratic transfer functions which correlates the incident wave spectrum with second-order forcing spectrum on the column.The sum-frequency QTFs for a TLP column are present,which are compared for some frequency pairs with those from a fully numerical procedure.Satisfactory agreement has been obtained.QTF spectra for a case study TLP column,generated using the semi-analytical solution are presented.Also given are the results for nonlinear wave field around the column.展开更多
The interaction between wave and horizontal and vertical plates is investigated by the boundary element method, and the relations of wave exciting force with plate thickness, submergence and length are obtained. It is...The interaction between wave and horizontal and vertical plates is investigated by the boundary element method, and the relations of wave exciting force with plate thickness, submergence and length are obtained. It is found that： 1） The efficient wave exciting force exists while plate submergence is less than 0.5 m, and the plate is very thin with order O（0.005 m）. 2） The maximum heave wave exciting force exists, and it is the main factor for surface and submerged horizontal plate while the roll force can be ignored. 3） The maximum sway wave exciting force exists, it is the main factor for surface or submerged vertical plate, and the roll force is about 20 times of horizontal plate.展开更多
A 2-D time-domain numerical coupled model is developed to obtain an efficient method for nonlinear wave forces on a fixed box-shaped ship in a harbor. The domain is divided into an inner domain and an outer domain. Th...A 2-D time-domain numerical coupled model is developed to obtain an efficient method for nonlinear wave forces on a fixed box-shaped ship in a harbor. The domain is divided into an inner domain and an outer domain. The inner domain is the area beneath the ship and the flow is described by the simplified Euler equations. The other area is the outer domain and the flow is defined by the higher-order Boussinesq equations in order to consider the nonlinearity of the wave motions. Along the interface boundaries between the inner domain and the outer domain, the volume flux is assumed to be continuous and the wave pressures are equal. Relevant physical experiment is conducted to validate the present model. It is shown that the numerical results agree with the experimental data. Compared with the coupled model with the flow in the inner domain governed by the Laplace equation, the present coupled model is more efficient and its solution procedure is more simple, which is particularly useful for the study on the effect of the nonlinear wave forces on a fixed box-shaped ship in a large harbor.展开更多
基金supported by the National Natural Science Foundation of China(Nos.51239008 and 51279130)
文摘This paper presents a study on the motion response of a tension-leg platform(TLP) under first-and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave force is calculated using the full-field quadratic transfer function(QTF). The coupled effect of the horizontal motions, such as surge, sway and yaw motions, and the set-down motion are taken into consideration by the nonlinear restoring matrix. The time-domain analysis with 50-yr random sea state is performed. A comparison of the results of different case studies is made to assess the influence of second-order wave force on the motions of the platform. The analysis shows that the second-order wave force has a major impact on motions of the TLP. The second-order difference-frequency wave force has an obvious influence on the low-frequency motions of surge and sway, and also will induce a large set-down motion which is an important part of heave motion. Besides, the second-order sum-frequency force will induce a set of high-frequency motions of roll and pitch. However, little influence of second-order wave force is found on the yaw motion.
基金funded by the National Natural Science Foundation of China(No.51809135)the Shandong Provincial Natural Science Foundation(No.ZR2018BEE 047)+1 种基金the National Natural Science Foundation of China–Shandong Joint Fund(No.U2006229)the SKL of HESS(No.HESS-1808).
文摘The selection of wave force models will significantly impact the structural responses of floating wind turbines.In this study,comparisons of wave force model effects on the structural responses and fatigue loads of a semi-submersible floating wind turbine(SFWT)were conducted.Simulations were performed by employing the Morison equation(ME)with linear or second-order wave kinematics and potential flow theory(PFT)with first-or second-order wave forces.A comparison of regular waves,irregular waves,and coupled wind/waves analyses with the experimental data showed that many of the simulation results and experimental data are relatively consistent.However,notable discrepancies are found in the response amplitude operators for platform heave,tower base bending moment,and tension in mooring lines.PFT models give more satisfactory results of heave but more significant discrepan-cies in tower base bending moment than the ME models.In irregular wave analyses,low-frequency resonances were captured by PFT models with second-order difference-frequency terms,and high-frequency resonances were captured by the ME models or PFT models with second-order sum-frequency terms.These force models capture the response frequencies but do not reasonably predict the response amplitudes.The coupled wind/waves analyses showed more satisfactory results than the wave-only analyses.However,an important detail to note is that this satisfactory result is based on the overprediction of wind-induced responses.
文摘-In this paper, an analytical solution in the outer region of finite water depth is derived for the second-order diffraction potential, which gives a clear physical meaning of the wave transmission and reflection characteristics in the far field. A numerical method-simple Green's function technique-for calculating the second-order diffraction potential in the inner region is also described. Numerical results are provided for the second-order wave forces on a semi-submerged cylinder. It is found that the contribution of second-order diffraction potential to second-order wave forces is important. The effect of water depth and submerged depth on the wave force is also discussed.
基金supported by the New Cornerstone Science Foundation through the XPLORER PRIZE and the National Natural Science Foundation of China(Grant No.52088102).
文摘A numerical study based on a two-dimensional two-phase SPH(Smoothed Particle Hydrodynamics)model to analyze the action of water waves on open-type sea access roads is presented.The study is a continuation of the analyses presented by Chen et al.(2022),in which the sea access roads are semi-immersed.In this new configuration,the sea access roads are placed above the still water level,therefore the presence of the air phase becomes a relevant issue in the determination of the wave forces acting on the structures.Indeed,the comparison of wave forces on the open-type sea access roads obtained from the single and two-phase SPH models with the experimental results shows that the latter are in much better agreement.So in the numerical simulations,a two-phaseδ-SPH model is adopted to investigate the dynamical problems.Based on the numerical results,the maximum horizontal and uplifting wave forces acting on the sea access roads are analyzed by considering different wave conditions and geometries of the structures.In particular,the presence of the girder is analyzed and the differences in the wave forces due to the air cushion effects which are created below the structure are highlighted.
文摘In this paper, we will concern the existence, asymptotic behaviors and stability of forced pulsating waves for a Lotka-Volterra cooperative system with nonlocal effects under shifting habitats. By using the alternatively-coupling upper-lower solution method, we establish the existence of forced pulsating waves, as long as the shifting speed falls in a finite interval where the endpoints are obtained from KPP-Fisher speeds. The asymptotic behaviors of the forced pulsating waves are derived. Finally, with proper initial, the stability of the forced pulsating waves is studied by the squeezing technique based on the comparison principle.
基金National Natural Science Foundation of China under Grant Nos.51622803 and 51708064the National Key Research and Development Program of China under Grant No.2016YFE0200100
文摘The second-order effect of axial force on horizontal vibrating characteristics of a large-diameter pipe pile is theoretically investigated.Governing equations of the pile-soil system are established based on elastodynamics.Threedimensional wave equations of soil are decoupled through differential transformation and variable separation.Consequently,expressions of soil displacements and horizontal resistances can be obtained.An analytical solution of the pile is derived based on continuity conditions between the pile and soil,subsequently from which expressions of the complex impedances are deduced.Analyses are carried out to examine the second-order effect of axial force on the horizontal vibrating behavior of the pipe pile.Some conclusions can be summarized as follows： stiffness and damping factors are decreased with the application of axial force on the pile head; distributions of the pile horizontal displacement and rotation angle are regenerated due to the second-order effect of the applied axial force; and redistributions of the bending moment and shearing force occur due to the second-order effect of the applied axial force.
基金Project supported by the National Natural Science Foundation of China (No. 12272323)。
文摘Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.
基金Supported by National Natural Science Foundation of China(No.5990 90 0 5) National High Performance Computing Foundation of
文摘A numerical model of wave force upon continuous cylinder structures with a large diameter using the boundary element method (BEM) is presented. A numerical model of reflecting wave upon continuous cylinders was established on the basis of linear wave theory.The fundamental solution to the Helmholtz equation within an infinite strip area that explicitly satisfies two infinite parallel boundaries is used together with Radiation condition rather than the solution of an infinite area.According to the proposed theory and method,the computer programs have been composed in Visual C ++ Development Studio.Several examples show that the technique and its program are feasible and efficient.And the wave forces upon continuous cylinders can be decreased by as much as 14%～24% under a ratio of D/L= 0.09～0.19 compared with the square caissons.
文摘The results of design and experiment of a submerged semi-circular breakwater at the Yangtze estuary show that the submerged structure will be unsafe when the general empirical wave force formula for semi-circular breakwater is used in design. Therefore, a new calculation method for the wave forces acting on a submerged semi-circular structure is given in this paper, in which the wave force acting on the inside circumference of semi-circular arch is included, and the phase modification coefficient in the general empirical formula is adjusted as well. The new wave force calculation method has been Verified by the results of seven related physical model tests and adopted in the design of the south esturary jetty of the first stage project of Deep Channel Improvement Project of the Yangtze River Estuary, the total jetty length being 17.5 km.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51490672 and 51761135011)the financial supports by the National Natural Science Foundation of China(Grant No.51490673)the Petro China Innovation Foundation(Grant No.2016D-5007-0601)
文摘Numerical simulations are carried out for wave action on a submerged horizontal circular cylinder by means of a viscous fluid model, and it is focused on the examination of the discrepancies between the viscous fluid results and the potential flow solutions. It is found that the lift force resulted from rotational flow on the circular cylinder is always in anti-phase with the inertia force and induces the discrepancies between the results. The influence factors on the magnitude of the lift force, especially the correlation between the stagnation-point position and the wave amplitude, and the effect of the vortex shedding are investigated by further examination on the flow fields around the cylinder. The viscous numerical calculations at different wave frequencies showed that the wave frequency has also significant influence on the wave forces. Under higher frequency and larger amplitude wave action, vortex shedding from the circular cylinder will appear and influence the wave forces on the cylinder substantially.
基金This project was supported by the Research Fund for the Development of Harbor Engineering Design Specification,the Ministry of Communications of Chinathe Program for Changjiang Scholars and Innovation Research Team in University of China under contract No.IRT0420the Fok Ying Tung Education Foundation of China under contract No.81068.
文摘Wave forces induced by the interaction between the oblique incident wave and the breakwater with a partially perforated front wall is investigated. The fluid domain is divided into two sub-domains and the eigen-function expansion method is applied to expanding velocity potentials in each domain. In the eigen-expansion of the velocity potential, evanescent waves are included. Numerical results of the present model are compared with other theories and a good agreement can be found between them. Experimental data have been compared with the present theoretical results. The effect of the traverse wall on wave forces has been discussed in detail. On the basis of the linear wave theory, it is shown that in the range Of engineering practice, the incident angle of wave has small influence on wave forces on the unit length of perforated caisson.
基金National Natural Science Foundation of China under the Grant No.19732004
文摘For the computation of wave forces on structures, a B-spline expansion is applied to discretize the body surface, and represent the velocity potentials on the body surface. The expansion coefficients for the body geometry are determined by the Least Square Method, and the coefficients for velocity potentials by the Galerkin method. The method can give continuous description of velocity potentials and their derivatives on the whole smooth body surface. The method has been implemented, and numerical results show that the method gives very accurate results and its convergence is fast.
基金The project was financially supported by the National Natural Science Foundation of China under the Grant No. 19732004 the National Science Fund for Distinguished Young Scholars under the Grant No. 50029002
文摘A time-domain method is applied to simulate nonlinear wave diffraction around a surface piercing 3-D arbitrary body. The method involves the application of Taylor series expansions and the use of perturbation procedure to establish the corresponding boundary value problems with respect to a time-independent fluid domain. A boundary element method based on B-spline expansion is used to calculate the wave field at each time step, and the free surface boundary condition is satisfied to the second order of wave steepness by a numerical integration in time. An artificial damping layer is adopted on the free surface for the removal of wave reflection from the outer boundary. As an illustration, the method is used to compute the second-order wave forces and run-up on a surface-piercing circular cylinder. The present method is found to be accurate, computationally efficient, and numerically stable.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51279187 and 41174157)the Fundamental Research Funds for the Central Universities(Grant No.201262005)the Promotive Research Fund for Excellent Young and Middle-aged Scientists of Shandong Province(Grant No.BS2013HZ014)
文摘A series of experimental studies about the force of internal solitary wave and internal periodic wave on vertical cylinders have been carried out in a two-dimensional layered internal wave flume. The internal solitary waves are produced by means of gravitational collapse at the layer thickness ratio of 0.2, and the internal periodic waves are produced with rocker-flap wave maker at the layer thickness ratio of 0.93. The wave parameters are obtained through dyeing photography. The vertical cylinders of the same size are arranged in different depths. The horizontal force on each cylinder is measured and the vertical distribution rules are researched. The internal wave heights are changed to study the impact of wave heights on the force. The results show that the horizontal force of concave type internal solitary wave on vertical cylinder in the upper-layer fluid has the same direction as the wave propagating, while it has an opposite direction in the lower-layer. The horizontal force is not evenly distributed in the lower fluid. And the force at different depths increases along with wave height. Internal solitary wave can produce an impact load on the entire pile. The horizontal force of internal periodic waves on the vertical cylinders is periodically changed at the frequency of waves. The direction of the force is opposite in the upper and lower layers, and the value is close. In the upper layer except the depth close to the interface, the force is evenly distributed; but it tends to decrease with the deeper depth in the lower layer. A periodic shear load can be produced on the entire pile by internal periodic waves, and it may cause fatigue damage to structures.
基金The present work was financially supported by the Joint Fund of the National Natural Science Foundation of China the Hong Kong Science Research Bureau under contract No.49910161985 the Research Fund for the Development of Harbor Engineering Desig
文摘The reflection coefficient and the total horizontal forces of regular waves acting on theperforated caisson are experimentally investigated. The empirical relationship between reflection coefficient and the ratio of the total horizontal forces acting on the perforated caisson to those on solid vertical walls with the relative chamber width, relative water depth and porosity of perforated wall, etc. are given. Moreover, the results of the ratio of the total horizontal forces are also compared with formulas given by Chinese Harbour Design Criteria and Takahashi, which may be useful for the practical engineering application.
文摘Based on model tests, the lift and resultant forces on small square cylinders caused by waves (regular and irregular) and currents are analyzed in this paper. The lift and resultant force coefficients CL and Cf related to KC number and the effect of direction of wave propagation are also given, which may be useful for practical engineering application.
文摘A complete semi-analytical solution is obtained for second-order diffraction of plane bichromatic waves by a fixed truncated circular column.The fluid domain is divided into interior and exterior regions.In the exterior region,the second-order velocity potential is expressed in terms of‘locked-wave’and‘free-wave’ components,both are solved using Fourier and eigenfunction expansions.The re- sulting‘locked wave’potential is expressed by one-dimensional Green's integrals with oscillating integrands.In order to increase computational efficiency,the far-field part of the integrals are carried out analytically.Solutions in both regions are matched on the interface by the potential and its normal derivative continuity conditions.Based on the present approach,the sum-and difference-frequency potentials are efficiently evaluated and are used to generate the quadratic transfer functions which correlates the incident wave spectrum with second-order forcing spectrum on the column.The sum-frequency QTFs for a TLP column are present,which are compared for some frequency pairs with those from a fully numerical procedure.Satisfactory agreement has been obtained.QTF spectra for a case study TLP column,generated using the semi-analytical solution are presented.Also given are the results for nonlinear wave field around the column.
基金supported by Foundation of Science and Technology of Dalian (Grant No. 2008A16GX248)
文摘The interaction between wave and horizontal and vertical plates is investigated by the boundary element method, and the relations of wave exciting force with plate thickness, submergence and length are obtained. It is found that： 1） The efficient wave exciting force exists while plate submergence is less than 0.5 m, and the plate is very thin with order O（0.005 m）. 2） The maximum heave wave exciting force exists, and it is the main factor for surface and submerged horizontal plate while the roll force can be ignored. 3） The maximum sway wave exciting force exists, it is the main factor for surface or submerged vertical plate, and the roll force is about 20 times of horizontal plate.
基金supported by the National Natural Science Foundation of China(Grant Nos.50809008 and59979002)the Hong Kong Research Council (HKU7171/06E)+1 种基金the Open Foundation of Hunan Province Key Lab-oratory of Water & Sediment Science and Water Hazard Prevention (Grant No.2008SS04)the Dalian Science and Technology Foundation (Grant No.2007J23JH027)
文摘A 2-D time-domain numerical coupled model is developed to obtain an efficient method for nonlinear wave forces on a fixed box-shaped ship in a harbor. The domain is divided into an inner domain and an outer domain. The inner domain is the area beneath the ship and the flow is described by the simplified Euler equations. The other area is the outer domain and the flow is defined by the higher-order Boussinesq equations in order to consider the nonlinearity of the wave motions. Along the interface boundaries between the inner domain and the outer domain, the volume flux is assumed to be continuous and the wave pressures are equal. Relevant physical experiment is conducted to validate the present model. It is shown that the numerical results agree with the experimental data. Compared with the coupled model with the flow in the inner domain governed by the Laplace equation, the present coupled model is more efficient and its solution procedure is more simple, which is particularly useful for the study on the effect of the nonlinear wave forces on a fixed box-shaped ship in a large harbor.
