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
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
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
Wave forces on two side-by-side boxes in close proximity under wave actions were analyzed using the OpenFOAM package.The upstream box heaved freely under wave actions,whereas the downstream box remained fixed.For comp...Wave forces on two side-by-side boxes in close proximity under wave actions were analyzed using the OpenFOAM package.The upstream box heaved freely under wave actions,whereas the downstream box remained fixed.For comparison,a configuration in which both boxes were fixed was also considered.The effects of the heave motion of the upstream box on the wave loads,including the horizontal wave forces,vertical wave forces,and moments on the boxes,were the focus of this study.Numerical analyses showed that all frequencies at which the maximum horizontal wave forces,maximum vertical wave forces,and maximum moment appeared are dependent on the heave motion of the upstream box and that the effects of the heave motion on these frequencies are different.Furthermore,these frequencies were observed to deviate from the corresponding fluid resonant frequency.Moreover,the heave motion of the upstream box reduced the wave forces acting on both boxes and altered the variation trends of the wave forces with the incident wave frequency.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
A three dimensional numerical model of nonlinear wave action on a quasi-ellipse caisson in a time domain was developed in this paper. Navier-Stokes equations were solved by the finite difference method, and the volume...A three dimensional numerical model of nonlinear wave action on a quasi-ellipse caisson in a time domain was developed in this paper. Navier-Stokes equations were solved by the finite difference method, and the volume of fluid （VOF） method was employed to trace the free surface. The partial cell method was used to deal with the irregular boundary typical of this type of problem during first-time wave interaction with the structure, and a satisfactory result was obtained. The numerical model was verified and used to investigate the effects of the relative wave height H/d, relative caisson width kD, and relative length-width ratio B/D on the wave forces of the quasi-ellipse caisson. It was shown that the relative wave height H/d has a significant effect on the wave forces of the caisson. Compared with the non-dimensional inline wave force, the relative length-width ratio BID was shown to have significant influence on the non-dimensional transverse wave force.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
In order to understand the wave forces and moments on a gravity pier foundation which consists of an upper column and a bottom gravity base,a model experiment with a scale of 1:60 has been conducted in a laboratory fl...In order to understand the wave forces and moments on a gravity pier foundation which consists of an upper column and a bottom gravity base,a model experiment with a scale of 1:60 has been conducted in a laboratory flume.A corresponding numerical calculation by using the boundary element method has been carried out to provide a comparative analysis.It is shown by the comparisons that the numerical wave forces and moments agree well with the experimental results.It is proved that the wave forces and moments acting on the foundation are completely in their inertia dominative areas for wave loads.With the diffraction effects considered into the inertia item,appropriate inertia coefficients are assessed by the experimental results for the inertia item of the Morison equation.The formula of the inertia item can be used to estimate wave forces and moments on such gravity foundations.展开更多
In this paper, a numerical model is established for estimating the wave forces on a submerged horizontal circular cylinder. For predicting the wave motion, a set of two dimensional Navier Stokes equations is solved ...In this paper, a numerical model is established for estimating the wave forces on a submerged horizontal circular cylinder. For predicting the wave motion, a set of two dimensional Navier Stokes equations is solved numerically with a finite element method. In order to track the moving non linear wave surface boundary, the Navier Stokes equations are discretized in a moving mesh system. After each computational time step, the mesh is modified according to the changed wave surface boundary. In order to stabilize the numerical procedure, a three step finite element method is applied in the time integration. The water sloshing in a tank and wave propagation over a submerged bar are simulated for the first time to validate the present model. The computational results agree well with the analytical solution and the experimental data. Finally, the model is applied to the simulation of interaction between waves and a submerged horizontal circular cylinder. The effects of the KC number and the cylinder depth on the wave forces are studied.展开更多
This paper presents an analytical formula for estimating the longitudinal wave forces on a large roundended caisson foundation. The establishment of the formula is based on the superposition of the theoretical formula...This paper presents an analytical formula for estimating the longitudinal wave forces on a large roundended caisson foundation. The establishment of the formula is based on the superposition of the theoretical formula of wave forces on a large circular cylinder and the empirical formula of wave forces on a large rectangular cylinder. With the formula transformed into an inertial force form, a specific inertia coefficient with an exact expression is extracted from the formula. The numerical calculations of the wave forces on round-ended cylinders are carried out by the boundary-element method. The undetermined coefficients in the expression of the inertial coefficient are determined by the numerical results. It is obvious that the numerical values can be well expressed by the computation values from the established formula. By a model experiment carried out in laboratory wave flume, the correctness of the analytical formula is further verified by the measured wave forces on a test model of a round-ended bridge caisson foundation. The comparison shows that the experimental forces can be approximately estimated by this simple calculation method.展开更多
An experimental investigation of irregular wave forces on quasi-ellipse caisson structures is presented. Irregular waves were generated based on the Jonswap spectrum with two significant wave heights, and the spectrum...An experimental investigation of irregular wave forces on quasi-ellipse caisson structures is presented. Irregular waves were generated based on the Jonswap spectrum with two significant wave heights, and the spectrum peak periods range from 1.19 s to 1.81 s. Incident wave directions relative to the centre line of the multiple caissons are from 0＆#176; to 22.5＆#176;. The spacing between caissons ranges from 2 to 3 times that of the width of the caisson. The effects of these parameters on the wave forces of both the perforated and non-perforated caissons were compared and analyzed. It was found that the perforated caisson can reduce wave forces, especially in the transverse direction. Furthermore, the relative interval and incident wave direction have significant effects on the wave forces in the case of multiple caissons.展开更多
A three-step finite element method (FEM) together with Large Eddy Simulation (LES) is applied to incompressible turbulent flow around seabed pipelines at relatively high Reynolds numbers. Both two dimensional and thre...A three-step finite element method (FEM) together with Large Eddy Simulation (LES) is applied to incompressible turbulent flow around seabed pipelines at relatively high Reynolds numbers. Both two dimensional and three-dimensional numerical simulation is carried out to determine the three-dimensional effect. The results of numerical simulation agree quite well with the wave forces acting on pipeline models measured in physical model test.展开更多
- In this paper, an engineering method is employed to calculate the horizontal and vertical wave forces on the mat of the submersible platform under Froude-Krylov hypothesis. According to some model tests, appropriate...- In this paper, an engineering method is employed to calculate the horizontal and vertical wave forces on the mat of the submersible platform under Froude-Krylov hypothesis. According to some model tests, appropriate diffraction coefficients are selected. And the results of the formulae given in the paper agree satisfactorily with those experimental data now available. The proposed computational method is effective and convenient to use in evaluating the horizontal and vertical wave forces on the mat. An exmaple is also given in this paper. Finally, the effects of the vertical wave force on the platorm's sit-on-bottom stability are analyzed.展开更多
A new analytical method is proposed to analyze the force acting on a rectangular oscillating buoy due to linear waves.In the method a new analytical expression for the diffraction velocity potential is obtained first ...A new analytical method is proposed to analyze the force acting on a rectangular oscillating buoy due to linear waves.In the method a new analytical expression for the diffraction velocity potential is obtained first by use of theeigenfunction expansion method and then the wave excitation force is calculated by use of the known incident wavepotential and the diffraction potential. Compared with the classical analytical method, it can be seen that the presentmethod is simpler for a two-dimensional problem due to the comparable effort needed for the computation ofdiffraction potential and for that of radiated potential. To verify the correctness of the method, a classical example inthe reference is recomputed and the obtained results are in good accordance with those by use of other methods,which shows that the present method is correct.展开更多
Offshore structures are generally classified as small-scale structures or large-scale structures.Their wave forces are then estimated by Morison equation and diffraction/radiation theories,respectively.However,the cla...Offshore structures are generally classified as small-scale structures or large-scale structures.Their wave forces are then estimated by Morison equation and diffraction/radiation theories,respectively.However,the classification criterion is not well quantified.In the present paper,a numerical wave flume is established to simulate the wave forces acting on a fixed and vertical surface-piercing circular cylinder under linear waves.By solving Navier–Stokes equation and Euler equation with free surface involved,respectively,the viscous force and inertia force are separated accurately.The variation of viscous force and inertia force with the cylinder diameter to wave length ratio is discussed in detail.The scale intervals for significant viscous and diffraction effects are given.The error caused by neglecting viscous and diffraction forces is quantitatively analyzed.Based on these analysis,the concept of medium-scale structure is proposed and the classification criteria for small-,medium-and large-scale structures are given.In the meantime,the estimation methods of wave forces for different scales of structures are suggested.展开更多
In this paper a 3D numerical model was developed to study the complicated interaction between waves and a set of tandem fixed cylinders.The fluid was considered to be inviscid and irrotational.Therefore,the Helmholtz ...In this paper a 3D numerical model was developed to study the complicated interaction between waves and a set of tandem fixed cylinders.The fluid was considered to be inviscid and irrotational.Therefore,the Helmholtz equation was used as a governing equation.The boundary element method（BEM） was adopted to discretize the relevant equations.Open boundaries were used in far fields of the study domain.Linear waves were generated and propagated towards tandem fixed cylinders to estimate the forces applied on them.Special attention was paid to consideration of the effect on varying non-dimensional cylinder radius and distance between cylinders,ka and kd on forces and trapped modes.The middle cylinder wave forces and trapped modes in a set of nine tandem cylinders were validated utilizing analytical data.The comparisons confirm the accuracy of the model.The results of the inline wave force estimation on n tandem cylinders show that the critical cylinder in the row is the middle one for odd numbers of cylinders.Furthermore the results show that the critical trapped mode effect occurs for normalized cylinder radiuses close to 0.5 and 1.0.Finally the force estimation for n tandem cylinders confirms that force amplitude of the middle cylinder versus normalized separation distance fluctuates about that of a single cylinder.展开更多
To study on the numerical simulation calculation reliability of sea-crossing bridge under complex wave forces,the paper applied GPS deformation monitoring and numerical simulation calculation by researching Qingdao Ji...To study on the numerical simulation calculation reliability of sea-crossing bridge under complex wave forces,the paper applied GPS deformation monitoring and numerical simulation calculation by researching Qingdao Jiaozhou Bay Sea-Crossing Bridge.The db3 wavelet three-layer decomposition was used on the horizontal movement of the sea-crossing bridge and the wind speed of the waves to analyze their correlation.The complex wave forces value of Qingdao Jiaozhou Bay Sea-Crossing Bridge was loaded on FLAC3D software successfully to make numerical simulation calculation of bridge deformation.Since the accuracy of the GPS deformation monitoring reaches millimeter level,it was used to monitor the exact value of the bridge deformation to judge the reliability of numerical simulation.The relative errors of displacement in X,Y and Z directions were between 33%and 41%through comparison.It could be seen that the numerical simulation error was relatively large,which was mainly due to various environmental factors and the deviation of applied wave forces.However,numerical simulation generally reflects the deformation law of the sea-crossing bridge under complex wave forces,providing an effectively technical support for the safe operation assessment of the sea-crossing bridge.展开更多
China's newly enacted Breakwater Design Specifications(JTS154-2011) explicitly state that breakwaters with water depths greater than 20 m are categorized as deep-water breakwaters, and emphasize that design princi...China's newly enacted Breakwater Design Specifications(JTS154-2011) explicitly state that breakwaters with water depths greater than 20 m are categorized as deep-water breakwaters, and emphasize that design principles, methods and construction requirements are different from those of common shallow water breakwaters. However, the specifications do not make any mention of how to choose wave force calculation methods of deep-water breakwaters. To study the feasibility of different formulae for wave force estimation of deep water combined breakwaters, the wave force calculated by the Sainflou's, Goda's, modified Goda's and specifications' methods are compared for various water depths and wave heights in this paper. The calculated results are also compared with experimental data. The total horizontal forcing and the pattern of pressure distributions are presented. Comparisons show that the wave pressure distributions by the four methods are similar, but the total horizontal forces are different. The results obtained by the Goda's method and the specified formulae are much closer to the experimental data. As for the wave force estimation for the deepwater mixed embankment foundation bed parapet, the Goda's formula is applied in the case with a water depth of less than 42 m. The Specifications method is suitable for standing waves. In the wave force estimates of breastworks, Sainflou's and the modified Gaoda's formulae are no longer applicable for the foundation bed of mixed embankment.展开更多
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.
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 National Key Research and Development Program(Grant No.2017YFC1404200)the National Natural Science Foundation of China(Grant Nos.51911530205 and 51809039)+4 种基金the Natural Science Foundation of Jiangsu Province(Grant No.BK20201455)the Natural Science Foundation of the Jiangsu Higher Education Institutions(Grant No.20KJD170005)the Qing Lan Project of Jiangsu Universities.This work is also partially supported by UK EPSRC(Grant No.EP/T026782/1)the Royal Academy of Engineering(Grant No.UKCIAPP/73)the Royal Society(Grant No.IEC\NSFC\181321).
文摘Wave forces on two side-by-side boxes in close proximity under wave actions were analyzed using the OpenFOAM package.The upstream box heaved freely under wave actions,whereas the downstream box remained fixed.For comparison,a configuration in which both boxes were fixed was also considered.The effects of the heave motion of the upstream box on the wave loads,including the horizontal wave forces,vertical wave forces,and moments on the boxes,were the focus of this study.Numerical analyses showed that all frequencies at which the maximum horizontal wave forces,maximum vertical wave forces,and maximum moment appeared are dependent on the heave motion of the upstream box and that the effects of the heave motion on these frequencies are different.Furthermore,these frequencies were observed to deviate from the corresponding fluid resonant frequency.Moreover,the heave motion of the upstream box reduced the wave forces acting on both boxes and altered the variation trends of the wave forces with the incident wave frequency.
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.
基金Supported by the Science and Technology Program on Transportation Construction in Western China Ministry of Communications under Grant No.2004-328-832-51
文摘A three dimensional numerical model of nonlinear wave action on a quasi-ellipse caisson in a time domain was developed in this paper. Navier-Stokes equations were solved by the finite difference method, and the volume of fluid （VOF） method was employed to trace the free surface. The partial cell method was used to deal with the irregular boundary typical of this type of problem during first-time wave interaction with the structure, and a satisfactory result was obtained. The numerical model was verified and used to investigate the effects of the relative wave height H/d, relative caisson width kD, and relative length-width ratio B/D on the wave forces of the quasi-ellipse caisson. It was shown that the relative wave height H/d has a significant effect on the wave forces of the caisson. Compared with the non-dimensional inline wave force, the relative length-width ratio BID was shown to have significant influence on the non-dimensional transverse wave force.
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.
基金the Technology Project of Ministry of Transport of China(No.2011318494150)
文摘In order to understand the wave forces and moments on a gravity pier foundation which consists of an upper column and a bottom gravity base,a model experiment with a scale of 1:60 has been conducted in a laboratory flume.A corresponding numerical calculation by using the boundary element method has been carried out to provide a comparative analysis.It is shown by the comparisons that the numerical wave forces and moments agree well with the experimental results.It is proved that the wave forces and moments acting on the foundation are completely in their inertia dominative areas for wave loads.With the diffraction effects considered into the inertia item,appropriate inertia coefficients are assessed by the experimental results for the inertia item of the Morison equation.The formula of the inertia item can be used to estimate wave forces and moments on such gravity foundations.
文摘In this paper, a numerical model is established for estimating the wave forces on a submerged horizontal circular cylinder. For predicting the wave motion, a set of two dimensional Navier Stokes equations is solved numerically with a finite element method. In order to track the moving non linear wave surface boundary, the Navier Stokes equations are discretized in a moving mesh system. After each computational time step, the mesh is modified according to the changed wave surface boundary. In order to stabilize the numerical procedure, a three step finite element method is applied in the time integration. The water sloshing in a tank and wave propagation over a submerged bar are simulated for the first time to validate the present model. The computational results agree well with the analytical solution and the experimental data. Finally, the model is applied to the simulation of interaction between waves and a submerged horizontal circular cylinder. The effects of the KC number and the cylinder depth on the wave forces are studied.
基金the Technology Project of Ministry of Transport of China(No.2011318494150)
文摘This paper presents an analytical formula for estimating the longitudinal wave forces on a large roundended caisson foundation. The establishment of the formula is based on the superposition of the theoretical formula of wave forces on a large circular cylinder and the empirical formula of wave forces on a large rectangular cylinder. With the formula transformed into an inertial force form, a specific inertia coefficient with an exact expression is extracted from the formula. The numerical calculations of the wave forces on round-ended cylinders are carried out by the boundary-element method. The undetermined coefficients in the expression of the inertial coefficient are determined by the numerical results. It is obvious that the numerical values can be well expressed by the computation values from the established formula. By a model experiment carried out in laboratory wave flume, the correctness of the analytical formula is further verified by the measured wave forces on a test model of a round-ended bridge caisson foundation. The comparison shows that the experimental forces can be approximately estimated by this simple calculation method.
基金Foundation item： Supported by the National Natural Science Foundation of China under Grant No. 51109032, and the National Natural Science Foundation of China under Grant No. 50921001.
文摘An experimental investigation of irregular wave forces on quasi-ellipse caisson structures is presented. Irregular waves were generated based on the Jonswap spectrum with two significant wave heights, and the spectrum peak periods range from 1.19 s to 1.81 s. Incident wave directions relative to the centre line of the multiple caissons are from 0＆#176; to 22.5＆#176;. The spacing between caissons ranges from 2 to 3 times that of the width of the caisson. The effects of these parameters on the wave forces of both the perforated and non-perforated caissons were compared and analyzed. It was found that the perforated caisson can reduce wave forces, especially in the transverse direction. Furthermore, the relative interval and incident wave direction have significant effects on the wave forces in the case of multiple caissons.
基金Part of results of a project financially supported by the State Key Laboratory of Coastal and Offshore Engineering of Dalian University of Technology
文摘A three-step finite element method (FEM) together with Large Eddy Simulation (LES) is applied to incompressible turbulent flow around seabed pipelines at relatively high Reynolds numbers. Both two dimensional and three-dimensional numerical simulation is carried out to determine the three-dimensional effect. The results of numerical simulation agree quite well with the wave forces acting on pipeline models measured in physical model test.
文摘- In this paper, an engineering method is employed to calculate the horizontal and vertical wave forces on the mat of the submersible platform under Froude-Krylov hypothesis. According to some model tests, appropriate diffraction coefficients are selected. And the results of the formulae given in the paper agree satisfactorily with those experimental data now available. The proposed computational method is effective and convenient to use in evaluating the horizontal and vertical wave forces on the mat. An exmaple is also given in this paper. Finally, the effects of the vertical wave force on the platorm's sit-on-bottom stability are analyzed.
基金This work Was supported by the High Tech Research and Development(863)Program of China under Grant No.2003AA5 16010the Chinese Academy of Science Pilot Project of the National Knowledge Innovation Program under Grant No.KGCX2-SW-305Chinese National Science Fund for Distinguished Young Scholars under Grant No.50125924.
文摘A new analytical method is proposed to analyze the force acting on a rectangular oscillating buoy due to linear waves.In the method a new analytical expression for the diffraction velocity potential is obtained first by use of theeigenfunction expansion method and then the wave excitation force is calculated by use of the known incident wavepotential and the diffraction potential. Compared with the classical analytical method, it can be seen that the presentmethod is simpler for a two-dimensional problem due to the comparable effort needed for the computation ofdiffraction potential and for that of radiated potential. To verify the correctness of the method, a classical example inthe reference is recomputed and the obtained results are in good accordance with those by use of other methods,which shows that the present method is correct.
基金This work was supported by the National Key R&D Program of China(Grant 2017yfc1404200)the National Natural Science Foundation of China(Grant 11572332)and the Strategic Priority Research Program of the Chinese Academy of Sciences(Grants xdb22040203 and xda22OOOOOO).
文摘Offshore structures are generally classified as small-scale structures or large-scale structures.Their wave forces are then estimated by Morison equation and diffraction/radiation theories,respectively.However,the classification criterion is not well quantified.In the present paper,a numerical wave flume is established to simulate the wave forces acting on a fixed and vertical surface-piercing circular cylinder under linear waves.By solving Navier–Stokes equation and Euler equation with free surface involved,respectively,the viscous force and inertia force are separated accurately.The variation of viscous force and inertia force with the cylinder diameter to wave length ratio is discussed in detail.The scale intervals for significant viscous and diffraction effects are given.The error caused by neglecting viscous and diffraction forces is quantitatively analyzed.Based on these analysis,the concept of medium-scale structure is proposed and the classification criteria for small-,medium-and large-scale structures are given.In the meantime,the estimation methods of wave forces for different scales of structures are suggested.
文摘In this paper a 3D numerical model was developed to study the complicated interaction between waves and a set of tandem fixed cylinders.The fluid was considered to be inviscid and irrotational.Therefore,the Helmholtz equation was used as a governing equation.The boundary element method（BEM） was adopted to discretize the relevant equations.Open boundaries were used in far fields of the study domain.Linear waves were generated and propagated towards tandem fixed cylinders to estimate the forces applied on them.Special attention was paid to consideration of the effect on varying non-dimensional cylinder radius and distance between cylinders,ka and kd on forces and trapped modes.The middle cylinder wave forces and trapped modes in a set of nine tandem cylinders were validated utilizing analytical data.The comparisons confirm the accuracy of the model.The results of the inline wave force estimation on n tandem cylinders show that the critical cylinder in the row is the middle one for odd numbers of cylinders.Furthermore the results show that the critical trapped mode effect occurs for normalized cylinder radiuses close to 0.5 and 1.0.Finally the force estimation for n tandem cylinders confirms that force amplitude of the middle cylinder versus normalized separation distance fluctuates about that of a single cylinder.
基金supported by the Natural Science Foundation of Shandong Province(No.ZR2020MD024)。
文摘To study on the numerical simulation calculation reliability of sea-crossing bridge under complex wave forces,the paper applied GPS deformation monitoring and numerical simulation calculation by researching Qingdao Jiaozhou Bay Sea-Crossing Bridge.The db3 wavelet three-layer decomposition was used on the horizontal movement of the sea-crossing bridge and the wind speed of the waves to analyze their correlation.The complex wave forces value of Qingdao Jiaozhou Bay Sea-Crossing Bridge was loaded on FLAC3D software successfully to make numerical simulation calculation of bridge deformation.Since the accuracy of the GPS deformation monitoring reaches millimeter level,it was used to monitor the exact value of the bridge deformation to judge the reliability of numerical simulation.The relative errors of displacement in X,Y and Z directions were between 33%and 41%through comparison.It could be seen that the numerical simulation error was relatively large,which was mainly due to various environmental factors and the deviation of applied wave forces.However,numerical simulation generally reflects the deformation law of the sea-crossing bridge under complex wave forces,providing an effectively technical support for the safe operation assessment of the sea-crossing bridge.
基金supported by the Shandong Sci-tech Development Plan(Item No.2008GGB01099)
文摘China's newly enacted Breakwater Design Specifications(JTS154-2011) explicitly state that breakwaters with water depths greater than 20 m are categorized as deep-water breakwaters, and emphasize that design principles, methods and construction requirements are different from those of common shallow water breakwaters. However, the specifications do not make any mention of how to choose wave force calculation methods of deep-water breakwaters. To study the feasibility of different formulae for wave force estimation of deep water combined breakwaters, the wave force calculated by the Sainflou's, Goda's, modified Goda's and specifications' methods are compared for various water depths and wave heights in this paper. The calculated results are also compared with experimental data. The total horizontal forcing and the pattern of pressure distributions are presented. Comparisons show that the wave pressure distributions by the four methods are similar, but the total horizontal forces are different. The results obtained by the Goda's method and the specified formulae are much closer to the experimental data. As for the wave force estimation for the deepwater mixed embankment foundation bed parapet, the Goda's formula is applied in the case with a water depth of less than 42 m. The Specifications method is suitable for standing waves. In the wave force estimates of breastworks, Sainflou's and the modified Gaoda's formulae are no longer applicable for the foundation bed of mixed embankment.
