A three-dimensional numerical model based on the potential theory was developed to study the oblique wave action on vertical walls. A source term inside the domain was used to generate incident waves and outgoing wave...A three-dimensional numerical model based on the potential theory was developed to study the oblique wave action on vertical walls. A source term inside the domain was used to generate incident waves and outgoing waves were dissipated by sponge layers and transmitted by radiation boundaries. The finite difference method was used to solve the governing equations and boundary conditions in the regular transformed domain in σ-coordinate. Satisfactory agreements between the numerical predictions and experimental results of wave force were obtained. It is concluded that the maximum wave force acting on the vertical walls is induced by the obliquely incident waves rather than the normally incident waves.展开更多
This study examines oblique wave motion over multiple submerged porous bars in front of a vertical wall. Based on linear potential theory, an analytical solution for the present problem is developed using matched eige...This study examines oblique wave motion over multiple submerged porous bars in front of a vertical wall. Based on linear potential theory, an analytical solution for the present problem is developed using matched eigenfunction expansions. A complex dispersion relation is adopted to describe the wave elevation and energy dissipation over submerged porous bars. In the analytical solution, no limitations on the bar number, bar size, and spacing between adjacent bars are set. The convergence of the analytical solution is satisfactory, and the correctness of the analytical solution is confirmed by an independently developed multi-domain BEM （boundary element method） solution. Numerical examples are presented to examine the reflection and transmission coefficients of porous bars, CR and Cv, respectively, for engineering applications. The calculation results show that when the sum of widths for all the porous bars is fixed, increasing the bar number can significantly improve the sheltering function of the bars. Increasing the bar height can cause more wave energy dissipation and lower CR and Cr. The spacing between adjacent bars and the spacing between the last bar and the vertical wall are the key parameters affecting CR and Ct. The proposed analytical method may be used to analyze the hydrodynamic performance of submerged porous bars in preliminary engineering designs.展开更多
With the method of separation of variables and the eigenfunction expansion employed, an analytical solution is presented for the radiation and diffraction of a rectangular structure with an opening near a vertical wal...With the method of separation of variables and the eigenfunction expansion employed, an analytical solution is presented for the radiation and diffraction of a rectangular structure with an opening near a vertical wall in oblique seas, in which the unknown coefficients are determined by the boundary conditions and matching requirement on the interface. The effects of the width of the opening and the angle of incidence on the hydrodynamic characteristics of a rectangular structure with an opening near a vertical wall are mainly studied. The comparisons of the calculation results with wall-present and with wall-absent are also made. The results indicate that the variation trends of the heave added mass and excitation force with wall-present are almost the same as those with wall-absent, and that the peak values in the former case are obviously larger than those in the latter due to the reflection of the vertical wall.展开更多
In order to investigate the energy absorption characteristics of multi-cell polygonal tubes with different cross-sectional configurations,firstly,the theoretical formulae of the mean crushing force under axial load fo...In order to investigate the energy absorption characteristics of multi-cell polygonal tubes with different cross-sectional configurations,firstly,the theoretical formulae of the mean crushing force under axial load for four multi-cell polygonal tubes were derived by combining the Super Folding Element theory with Zhang’s research results.These formulae can be used to validate the numerical model and quickly evaluate the energy absorption ability of multi-cell polygonal tubes.Furthermore,a comparative study on the energy absorption performance of eight multi-cell polygonal tubes under axial and oblique loads was conducted.The results show that all tubes have a stable mixed deformation mode under axial load.The multi-cell decagon tube has better energy-absorption ability compared with other tubes.Whenθis less than 10°,all the tubes maintain a stable deformation mode,and the multi-cell decagon tube also has the biggest crushing force efficiency and specific energy absorption among these eight tubes;meanwhile compared with the results atθ=0°,the specific energy absorption of all tubes decreases by about 8%-21%,while the crushing force efficiency increases by 20%-56%.However,at large angles 20°and 30°,all of the tubes collapse in bending modes and lose their effectiveness at energy absorption.展开更多
Regular and irregular wave forces acting on vertical walls are studied by a previously developed numerical model. The computed wave forces are compared with the available experimental data to verify the numerical mode...Regular and irregular wave forces acting on vertical walls are studied by a previously developed numerical model. The computed wave forces are compared with the available experimental data to verify the numerical model, and satisfactory agreements are obtained. The variation of wave forces with incident angles and the shape of simultaneous pressure distribution are investigated, and the comparisons between numerical results and Goda＇ s predictions are also carried out. It is concluded that the maximum wave forces acting on the unit length of vertical wall is often induced by the obliquely incident waves instead of normally incident waves, while Goda＇ s formula may be inapplicable for oblique wave incidence. The shape of simultaneous pressure distribution is not significantly influenced by incident angles, and it can be favorably predicted by Goda＇ s formula. When regular wave heights are taken as the same as irregular wave height H1%, the irregular wave forces Ph. 1% are slightly larger than regular wave forces in most cases.展开更多
The interaction of oblique incident waves with infinite number of perforated caissons is investigated. The fluid domain is divided into infinite sub-domains by the caissons, and eigen-function expansion is applied to ...The interaction of oblique incident waves with infinite number of perforated caissons is investigated. The fluid domain is divided into infinite sub-domains by the caissons, and eigen-function expansion is applied to expand velocity potentials in each domain. A phase relation is introduced for wave oscillation in each caisson, and the structure geometry is considered in constructing the models of reflection waves. The reflected waves with the present analysis include all of the waves traveling in different directions when incident wave period is short. Numerical examinations show that velocities at the inner and outer sides of the front walls of caissons ase close to each other, and reflection coefficients satisfy the energy conservation relation very well when porous effect parameter is infinite. Numerical results show that the reflection coefficients of oblique incident waves are smaller for shorter caissons at low frequency, and decrease with the increase of wave incident angle.展开更多
When an incoming water wave is parallel to a porous breakwater, a paradoxical phenomenon exists in that by strictly following the potential flow boundary condition of normal flux continuity on the interfaces, the wate...When an incoming water wave is parallel to a porous breakwater, a paradoxical phenomenon exists in that by strictly following the potential flow boundary condition of normal flux continuity on the interfaces, the water wave permeates the wall completely, regardless of breakwater porosity. To account for this paradoxical phenomenon when solving the problem of water waves obliquely impacting on a thin porous wall, a new partial-slipping boundary condition on the thin porous wall for potential flow is proposed. Analytical results show that when the water wave is parallel to a thin porous wall （i.e., the incident angle equals to 90~）, the transmitted wave side remains quiescent, i.e., the transmitted wave side does not capture any wave energy when no viscous effect exists. This reveals that the above-mentioned paradoxical investigated in this study, which provides proper boundary information. phenomenon disappears. The viscous boundary layer effect is also conditions on a thin porous wall for viscous flows and detailed flow展开更多
基金supported by the National Science Foundation of China for Distinguished Young Scholars under contract No.50025925the National Natural Science Foundation of China under contract No.50079001.
文摘A three-dimensional numerical model based on the potential theory was developed to study the oblique wave action on vertical walls. A source term inside the domain was used to generate incident waves and outgoing waves were dissipated by sponge layers and transmitted by radiation boundaries. The finite difference method was used to solve the governing equations and boundary conditions in the regular transformed domain in σ-coordinate. Satisfactory agreements between the numerical predictions and experimental results of wave force were obtained. It is concluded that the maximum wave force acting on the vertical walls is induced by the obliquely incident waves rather than the normally incident waves.
基金supported by the National Natural Science Foundation of China(Nos.51490675,51322903 and 51279224.)
文摘This study examines oblique wave motion over multiple submerged porous bars in front of a vertical wall. Based on linear potential theory, an analytical solution for the present problem is developed using matched eigenfunction expansions. A complex dispersion relation is adopted to describe the wave elevation and energy dissipation over submerged porous bars. In the analytical solution, no limitations on the bar number, bar size, and spacing between adjacent bars are set. The convergence of the analytical solution is satisfactory, and the correctness of the analytical solution is confirmed by an independently developed multi-domain BEM （boundary element method） solution. Numerical examples are presented to examine the reflection and transmission coefficients of porous bars, CR and Cv, respectively, for engineering applications. The calculation results show that when the sum of widths for all the porous bars is fixed, increasing the bar number can significantly improve the sheltering function of the bars. Increasing the bar height can cause more wave energy dissipation and lower CR and Cr. The spacing between adjacent bars and the spacing between the last bar and the vertical wall are the key parameters affecting CR and Ct. The proposed analytical method may be used to analyze the hydrodynamic performance of submerged porous bars in preliminary engineering designs.
基金supported by the National Natural Science Foundation of China(Grant Nos.51079082 and 51679132)the Nature Science Foundation of Shanghai City(Grant No.14ZR1419600)the Research Innovation Projects of 2013 Shanghai Postgraduate(Grant No.20131129)
文摘With the method of separation of variables and the eigenfunction expansion employed, an analytical solution is presented for the radiation and diffraction of a rectangular structure with an opening near a vertical wall in oblique seas, in which the unknown coefficients are determined by the boundary conditions and matching requirement on the interface. The effects of the width of the opening and the angle of incidence on the hydrodynamic characteristics of a rectangular structure with an opening near a vertical wall are mainly studied. The comparisons of the calculation results with wall-present and with wall-absent are also made. The results indicate that the variation trends of the heave added mass and excitation force with wall-present are almost the same as those with wall-absent, and that the peak values in the former case are obviously larger than those in the latter due to the reflection of the vertical wall.
基金Projects(U1334208,51405516,51275532)supported by the National Natural Science Foundation of ChinaProjects(2015zzts210,2016zzts331)supported by the Fundamental Research Funds for the Central Universities,China
文摘In order to investigate the energy absorption characteristics of multi-cell polygonal tubes with different cross-sectional configurations,firstly,the theoretical formulae of the mean crushing force under axial load for four multi-cell polygonal tubes were derived by combining the Super Folding Element theory with Zhang’s research results.These formulae can be used to validate the numerical model and quickly evaluate the energy absorption ability of multi-cell polygonal tubes.Furthermore,a comparative study on the energy absorption performance of eight multi-cell polygonal tubes under axial and oblique loads was conducted.The results show that all tubes have a stable mixed deformation mode under axial load.The multi-cell decagon tube has better energy-absorption ability compared with other tubes.Whenθis less than 10°,all the tubes maintain a stable deformation mode,and the multi-cell decagon tube also has the biggest crushing force efficiency and specific energy absorption among these eight tubes;meanwhile compared with the results atθ=0°,the specific energy absorption of all tubes decreases by about 8%-21%,while the crushing force efficiency increases by 20%-56%.However,at large angles 20°and 30°,all of the tubes collapse in bending modes and lose their effectiveness at energy absorption.
基金This researchis financially supported by the Natural National Science Foundation of China (Grant No.50079001)the Key problemof Science and Technology of 15th Five-year Plan"Study of Forecasting and Cautioning Tech-nique of Serious Marine Disaster Inshore"
文摘Regular and irregular wave forces acting on vertical walls are studied by a previously developed numerical model. The computed wave forces are compared with the available experimental data to verify the numerical model, and satisfactory agreements are obtained. The variation of wave forces with incident angles and the shape of simultaneous pressure distribution are investigated, and the comparisons between numerical results and Goda＇ s predictions are also carried out. It is concluded that the maximum wave forces acting on the unit length of vertical wall is often induced by the obliquely incident waves instead of normally incident waves, while Goda＇ s formula may be inapplicable for oblique wave incidence. The shape of simultaneous pressure distribution is not significantly influenced by incident angles, and it can be favorably predicted by Goda＇ s formula. When regular wave heights are taken as the same as irregular wave height H1%, the irregular wave forces Ph. 1% are slightly larger than regular wave forces in most cases.
文摘The interaction of oblique incident waves with infinite number of perforated caissons is investigated. The fluid domain is divided into infinite sub-domains by the caissons, and eigen-function expansion is applied to expand velocity potentials in each domain. A phase relation is introduced for wave oscillation in each caisson, and the structure geometry is considered in constructing the models of reflection waves. The reflected waves with the present analysis include all of the waves traveling in different directions when incident wave period is short. Numerical examinations show that velocities at the inner and outer sides of the front walls of caissons ase close to each other, and reflection coefficients satisfy the energy conservation relation very well when porous effect parameter is infinite. Numerical results show that the reflection coefficients of oblique incident waves are smaller for shorter caissons at low frequency, and decrease with the increase of wave incident angle.
基金supported by the National Science Council,(Grant No.NSC92-2611-E002-029)
文摘When an incoming water wave is parallel to a porous breakwater, a paradoxical phenomenon exists in that by strictly following the potential flow boundary condition of normal flux continuity on the interfaces, the water wave permeates the wall completely, regardless of breakwater porosity. To account for this paradoxical phenomenon when solving the problem of water waves obliquely impacting on a thin porous wall, a new partial-slipping boundary condition on the thin porous wall for potential flow is proposed. Analytical results show that when the water wave is parallel to a thin porous wall （i.e., the incident angle equals to 90~）, the transmitted wave side remains quiescent, i.e., the transmitted wave side does not capture any wave energy when no viscous effect exists. This reveals that the above-mentioned paradoxical investigated in this study, which provides proper boundary information. phenomenon disappears. The viscous boundary layer effect is also conditions on a thin porous wall for viscous flows and detailed flow
