In the present work, the improved version of the meshless singular boundary method(ISBM) is developed for analyzing the performance of bottom standing submerged permeable breakwaters in regular normally incident waves...In the present work, the improved version of the meshless singular boundary method(ISBM) is developed for analyzing the performance of bottom standing submerged permeable breakwaters in regular normally incident waves and in the proximity of a vertical wall. Both single and dual prismatic breakwaters of rectangular and trapezoidal forms are examined. The physical problem is cast in terms of the Laplace equation governing an irrotational flow and incompressible fluid motion with appropriate mixed type boundary conditions, and solved numerically using the ISBM. To model the permeability of the breakwaters fully absorbing boundary conditions are assumed. Numerical results are presented in terms of hydrodynamic quantities of the reflection coefficients. These are firstly validated against the results of a multi-domain boundary element method(BEM) developed independently for a previous study. The agreement between the results of the two methods is excellent. The coefficients of reflection are then computed and discussed for a variety of structural conditions including the breakwaters height, width, spacing, and absorbing permeability. Effects of the proximity of the vertical plane wall are also investigated. The breakwater's width is found to have only marginal effects compared with its height. Permeability tends to decrease the minimum reflections. These coefficients show periodic variations with the spacing relative to the wavelength. Trapezoidal breakwaters are found to be more cost-effective than the rectangular breakwaters. Dual breakwater systems are confirmed to perform much better than single structures.展开更多
A vertical 2-D numerical wave model was developed based on unsteady Reynolds equations. In this model, the k-epsilon models were used to close the Reynolds equations, and volume of fluid(VOF) method was used to recons...A vertical 2-D numerical wave model was developed based on unsteady Reynolds equations. In this model, the k-epsilon models were used to close the Reynolds equations, and volume of fluid(VOF) method was used to reconstruct the free surface. The model was verified by experimental data. Then the model was used to simulate solitary wave interaction with submerged, alternative submerged and emerged semi-circular breakwaters. The process of velocity field, pressure field and the wave surface near the breakwaters was obtained. It is found that when the semi-circular breakwater is submerged, a large vortex will be generated at the bottom of the lee side wall of the breakwater; when the still water depth is equal to the radius of the semi-circular breakwater, a pair of large vortices will be generated near the shoreward wall of the semi-circular breakwater due to wave impacting, but the velocity near the bottom of the lee side wall of the breakwater is always relatively small. When the semi-circular breakwater is emerged, and solitary wave cannot overtop it, the solitary wave surface will run up and down secondarily during reflecting from the breakwater. It can be further used to estate the diffusing and transportation of the contamination and transportation of suspended sediment.展开更多
The numerical investigation of regular waves interacting with a submerged horizontal twin-plate breakwater is pre- sented in this paper. A numerical model with an absorbing wave-maker is established based on the VOF m...The numerical investigation of regular waves interacting with a submerged horizontal twin-plate breakwater is pre- sented in this paper. A numerical model with an absorbing wave-maker is established based on the VOF method. The validity of the model is verified by experimental results. Comparisons between the numerical and experimental results show that beth the water surface profiles and the wave-induced pressures can be modeled accurately. Wave deformation over the breakwater, water particle velocities around the breakwater, and the wave-induced pressures on the structure are nu- merically investigated. Tile pressure amplitudes of the fundamental and second harmonies on the model surface are exanl- ined in various water depths. The computed and experimental results have revealed that the higher frequency components are generated at the onshore side of the breakwater. Furthermore, the computed results demonstrate a circulating flow formed at the onshore side of the breakwater.展开更多
Comprehensive experimental and numerical studies have been undertaken to investigate wave energy dissipation performance and main influencing factors of a lower arc-plate breakwater. The numerical model, which conside...Comprehensive experimental and numerical studies have been undertaken to investigate wave energy dissipation performance and main influencing factors of a lower arc-plate breakwater. The numerical model, which considers nonlinear interactions between waves and the arc-plate breakwater, has been constructed by using the velocity wave- generating method, the volume of fluid (VOF) method and the finite volume method. The results show that the relative width, relative height and relative submergence of the breakwater are three main influencing factors and have significant influence on wave energy dissipation of the lower arc-plate open breakwater. The transmission coefficient is found to decrease with the increasing relative width, and the minimum transmission coefficient is 0.15 when the relative width is 0.45. The reflection coefficient is found to vary slightly with the relative width, and the maximum reflection coefficient is 0.53 when the relative width is 0.45. The transmission and reflection coefficients are shown to increase with the relative wave height for approximately 85% of the experimental tests when the relative width is 0.19 0.45. The transmission coefficients at relative submergences of 0.04, 0.02 and 0 are clearly shown to be greater than those at relative submergences of 0.02 and 0.04, while the reflection coefficient exhibits the opposite relationship. After the wave interacts with the lower arc-plate breakwater, the wave energy is mainly converted into transmission, reflection and dissipation energies. The wave attenuation performance is clearly weakened for waves with greater heights and longer periods.展开更多
In this study, solitary waves passing over a submerged breakwater are investigated both experimentally and numerically. A total of 9 experimental conditions are carried out, including different incident wave heights a...In this study, solitary waves passing over a submerged breakwater are investigated both experimentally and numerically. A total of 9 experimental conditions are carried out, including different incident wave heights and water depths. Numerical simulations are performed using a high-order finite-difference model solving Navier–Stokes (N–S) equations. The predicted water wave elevation, velocity and pressure show good agreement with experimental data, verifying the accuracy and capacity of the numerical model. Furthermore, parametric studies are conducted by numerical modelling to examine the effects of the geometrical features of submerged dike on hydrodynamic characteristics around the breakwater.展开更多
In this study, characteristics of flow field and wave propagation near submerged breakwater on a sloping bed are investigated with numerical model. The governing equations of the vertical two-dimensional model are Rey...In this study, characteristics of flow field and wave propagation near submerged breakwater on a sloping bed are investigated with numerical model. The governing equations of the vertical two-dimensional model are Reynolds Averaged Navier Stokes equations. The Reynolds stress terms are closed by a nonlinear k - ε turbulence transportation model. The free surface is traced through the PILC-VOF method. The proposed numerical model is verified with experimental results. The numerical result shows that the wave profile may become more asymmetrical when wave propagates over breakwater. When wave crest propagates over breakwater, the anticlockwise vortex may generate. On the contrary, when wave hollow propagates over breakwater, the clockwise vortex may generate. Meanwhile, the influenced zone of vortex created by wave crest is larger than that created by wave hollow. All the maximum values of the turbulent kinetic energy, turbulent dissipation and eddy viscosity occur on the top of breakwater. Both the turbulent dissipation and eddy viscosity increase as the turbulent kinetic energy increases. Wave energy may rapidly decrease near the breakwater because turbulent dissipation increases and energy in lower harmonics is transferred into higher harmonics.展开更多
基金financially supported by the Direction Général des Enseignements et de la Formation Supérieure of Algeria(Grant CNEPRU No.G0301920140029)
文摘In the present work, the improved version of the meshless singular boundary method(ISBM) is developed for analyzing the performance of bottom standing submerged permeable breakwaters in regular normally incident waves and in the proximity of a vertical wall. Both single and dual prismatic breakwaters of rectangular and trapezoidal forms are examined. The physical problem is cast in terms of the Laplace equation governing an irrotational flow and incompressible fluid motion with appropriate mixed type boundary conditions, and solved numerically using the ISBM. To model the permeability of the breakwaters fully absorbing boundary conditions are assumed. Numerical results are presented in terms of hydrodynamic quantities of the reflection coefficients. These are firstly validated against the results of a multi-domain boundary element method(BEM) developed independently for a previous study. The agreement between the results of the two methods is excellent. The coefficients of reflection are then computed and discussed for a variety of structural conditions including the breakwaters height, width, spacing, and absorbing permeability. Effects of the proximity of the vertical plane wall are also investigated. The breakwater's width is found to have only marginal effects compared with its height. Permeability tends to decrease the minimum reflections. These coefficients show periodic variations with the spacing relative to the wavelength. Trapezoidal breakwaters are found to be more cost-effective than the rectangular breakwaters. Dual breakwater systems are confirmed to perform much better than single structures.
文摘A vertical 2-D numerical wave model was developed based on unsteady Reynolds equations. In this model, the k-epsilon models were used to close the Reynolds equations, and volume of fluid(VOF) method was used to reconstruct the free surface. The model was verified by experimental data. Then the model was used to simulate solitary wave interaction with submerged, alternative submerged and emerged semi-circular breakwaters. The process of velocity field, pressure field and the wave surface near the breakwaters was obtained. It is found that when the semi-circular breakwater is submerged, a large vortex will be generated at the bottom of the lee side wall of the breakwater; when the still water depth is equal to the radius of the semi-circular breakwater, a pair of large vortices will be generated near the shoreward wall of the semi-circular breakwater due to wave impacting, but the velocity near the bottom of the lee side wall of the breakwater is always relatively small. When the semi-circular breakwater is emerged, and solitary wave cannot overtop it, the solitary wave surface will run up and down secondarily during reflecting from the breakwater. It can be further used to estate the diffusing and transportation of the contamination and transportation of suspended sediment.
基金supported by the National Natural Science Foundation of China ( Grant Nos .50921001 and 51079025)
文摘The numerical investigation of regular waves interacting with a submerged horizontal twin-plate breakwater is pre- sented in this paper. A numerical model with an absorbing wave-maker is established based on the VOF method. The validity of the model is verified by experimental results. Comparisons between the numerical and experimental results show that beth the water surface profiles and the wave-induced pressures can be modeled accurately. Wave deformation over the breakwater, water particle velocities around the breakwater, and the wave-induced pressures on the structure are nu- merically investigated. Tile pressure amplitudes of the fundamental and second harmonies on the model surface are exanl- ined in various water depths. The computed and experimental results have revealed that the higher frequency components are generated at the onshore side of the breakwater. Furthermore, the computed results demonstrate a circulating flow formed at the onshore side of the breakwater.
基金supported by the NSFC-Shandong Joint Fund(Grant Nos.U1706220 and U1806227)the National Natural Science Foundation of China(Grant Nos.51709140 and 51879019)the Key Laboratory of Coastal Disasters and Defence of Ministry of Education(Grant No.201703)
文摘Comprehensive experimental and numerical studies have been undertaken to investigate wave energy dissipation performance and main influencing factors of a lower arc-plate breakwater. The numerical model, which considers nonlinear interactions between waves and the arc-plate breakwater, has been constructed by using the velocity wave- generating method, the volume of fluid (VOF) method and the finite volume method. The results show that the relative width, relative height and relative submergence of the breakwater are three main influencing factors and have significant influence on wave energy dissipation of the lower arc-plate open breakwater. The transmission coefficient is found to decrease with the increasing relative width, and the minimum transmission coefficient is 0.15 when the relative width is 0.45. The reflection coefficient is found to vary slightly with the relative width, and the maximum reflection coefficient is 0.53 when the relative width is 0.45. The transmission and reflection coefficients are shown to increase with the relative wave height for approximately 85% of the experimental tests when the relative width is 0.19 0.45. The transmission coefficients at relative submergences of 0.04, 0.02 and 0 are clearly shown to be greater than those at relative submergences of 0.02 and 0.04, while the reflection coefficient exhibits the opposite relationship. After the wave interacts with the lower arc-plate breakwater, the wave energy is mainly converted into transmission, reflection and dissipation energies. The wave attenuation performance is clearly weakened for waves with greater heights and longer periods.
基金financially supported by the National Natural Science Foundation of China(Grant No.51679212)Zhejiang Provincial Natural Science Foundation of China(Grant No.LR16E090002)+1 种基金the Fundamental Research Funds for the Central Universities(Grant No.2018QNA4041)the Tang Scholar
文摘In this study, solitary waves passing over a submerged breakwater are investigated both experimentally and numerically. A total of 9 experimental conditions are carried out, including different incident wave heights and water depths. Numerical simulations are performed using a high-order finite-difference model solving Navier–Stokes (N–S) equations. The predicted water wave elevation, velocity and pressure show good agreement with experimental data, verifying the accuracy and capacity of the numerical model. Furthermore, parametric studies are conducted by numerical modelling to examine the effects of the geometrical features of submerged dike on hydrodynamic characteristics around the breakwater.
基金The National Natural Science Foundation of China under contract Nos 50979008 and 50909009Program for Hunan Province Key Laboratory of WaterSediment Sciences & Flood Hazard Prevention and Open Research Fund Program of State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering,Hohai University No.2008490911
文摘In this study, characteristics of flow field and wave propagation near submerged breakwater on a sloping bed are investigated with numerical model. The governing equations of the vertical two-dimensional model are Reynolds Averaged Navier Stokes equations. The Reynolds stress terms are closed by a nonlinear k - ε turbulence transportation model. The free surface is traced through the PILC-VOF method. The proposed numerical model is verified with experimental results. The numerical result shows that the wave profile may become more asymmetrical when wave propagates over breakwater. When wave crest propagates over breakwater, the anticlockwise vortex may generate. On the contrary, when wave hollow propagates over breakwater, the clockwise vortex may generate. Meanwhile, the influenced zone of vortex created by wave crest is larger than that created by wave hollow. All the maximum values of the turbulent kinetic energy, turbulent dissipation and eddy viscosity occur on the top of breakwater. Both the turbulent dissipation and eddy viscosity increase as the turbulent kinetic energy increases. Wave energy may rapidly decrease near the breakwater because turbulent dissipation increases and energy in lower harmonics is transferred into higher harmonics.
