In this paper, the hydrodynamic efficiency of a floating breakwater system is experimentally studied by use of physical models. Regular waves with wide ranges of wave heights and periods are tested. The efficiency of ...In this paper, the hydrodynamic efficiency of a floating breakwater system is experimentally studied by use of physical models. Regular waves with wide ranges of wave heights and periods are tested. The efficiency of the breakwater is presented as a function of the wave transmission, reflection, and energy dissipation coefficients. Different parameters affecting the breakwater efficiency are investigated, e.g. the number of the under connected vertical plates, the length of the mooring wire, and the wave length. It is found that, the transmission coefficient kt decreases with the increase of the relative breakwater width B/L, the number of plates n and the relative wire length l/h, while the reflection coefficient kr takes the opposite trend. Therefore, it is possible to achieve kt values smaller than 0.25 and kr values larger than 0.80 when B/L is larger than 0.25 for the case of l/h-1.5 and n=4. In addition, empirical equations used for estimating the transmission and reflection coefficients are developed by using the dimensionless analysis, regression analysis and measured data and verified by different theoretical and experimental results.展开更多
A series of regular and irregular wave experiments are conducted to study the reflective and transmitting performances of quarter circular breakwater （QCB） in comparison with those of semi-circular breakwater （SCB...A series of regular and irregular wave experiments are conducted to study the reflective and transmitting performances of quarter circular breakwater （QCB） in comparison with those of semi-circular breakwater （SCB）. Based on regular wave tests, the reflection and transmission characteristics of QCB are analyzed and a few influencing factors are investigated. Then, the wave energy dissipation as wave passing over the breakwater is discussed based on the hydraulic coefficients of QCB and SCB. In irregular wave experiments, the reflection coefficients of QCB and their spectrums are studied. Finally, the comparisons between the experimental results and numerical simulations for QCB under regular and irregular wave conditions are presented.展开更多
We establish the existence of a global solution to a regular reflection of a shock hitting a ramp for the pressure gradient system of equations. The set-up of the reflection is the same as that of Mach＇s experiment f...We establish the existence of a global solution to a regular reflection of a shock hitting a ramp for the pressure gradient system of equations. The set-up of the reflection is the same as that of Mach＇s experiment for the compressible Euler system, i.e., a straight shock hitting a ramp. We assume that the angle of the ramp is close to 90 degrees. The solution has a reflected bow shock wave, called the diffraction of the planar shock at the compressive corner, which is mathematically regarded as a free boundary in the self-similar variable plane. The pressure gradient system of three equations is a subsystem, and an approximation, of the full Euler system, and we offer a couple of derivations.展开更多
When the high-pressure gas is exhausted to the vacuum chamber from the nozzle,the underexpanded supersonic jet contained with the Mach disk is generally formed.The eventual purpose of this study is to clarify the unst...When the high-pressure gas is exhausted to the vacuum chamber from the nozzle,the underexpanded supersonic jet contained with the Mach disk is generally formed.The eventual purpose of this study is to clarify the unsteady phenomenon of the underexpanded free jet when the back pressure continuously changes with time.The characteristic of the Mach disk has been clarified in consideration of the diameter and position of it by the numerical analysis in this paper.The sonic jet of the exit Mach number Me=1 is assumed and the axisymmetric conservational equation is solved by the TVD method in the numerical calculation.The diameter and position of the Mach disk differs with the results of a steady jet and the influence on the continuously changing of the back pressure is evidenced from the comparison with the case of steady supersonic jet.展开更多
Using a discretized finite difference method, a numerical model was developed to study the interaction of regular waves with a perforated breakwater. Considering a non-viscous, non-rotational fluid, the governing equa...Using a discretized finite difference method, a numerical model was developed to study the interaction of regular waves with a perforated breakwater. Considering a non-viscous, non-rotational fluid, the governing equations of Laplacian velocity potential were developed, and specific conditions for every single boundary were defined. The final developed model was evaluated based on an existing experimental result. The evaluated model was used to simulate the condition for various wave periods from 0.6 to 2 s. The reflection coefficient and transmission coefficient of waves were examined with different breakwater porosities, wave steepnesses, and angular frequencies. The results show that the developed model can suitably present the effect of the structural and hydraulic parameters on the reflection and transmission coefficients. It was also found that with the increase in wave steepness, the reflection coefficient increased logarithmically, while the transmission coefficient decreased logarithmically.展开更多
When the pressure ratio increases from the perfectly expanded condition to the third limited condition in which a normal shock is located on the exit plane, shock wave configurations outside the nozzle can be further ...When the pressure ratio increases from the perfectly expanded condition to the third limited condition in which a normal shock is located on the exit plane, shock wave configurations outside the nozzle can be further assorted as no shock wave on the perfectly expanded condition, weak oblique shock reflection in the regular reflection （RR） pressure ratio condition, shock reflection hysteresis in the dual-solution domain of pressure ratio condition, Mach disk configurations in the Mach reflection （MR） pressure ratio condition, the strong oblique shock wave configurations in the corresponding condition, and a normal shock forms on the exit plane in the third limited con- dition. Every critical pressure ratio, especially under regular reflection and Mach reflection pressure ratio conditions, is deduced in the paper according to shock wave reflection theory. A hysteresis phenomenon is also theoretically possible in the dual-solution domain. For a planar Laval nozzle with the cross-section area ratio being 5, different critical pressure ratios are counted in these con- ditions, and numerical simulations are made to demonstrate these various shock wave configurations outside the nozzle. Theoretical analysis and numerical simulations are made to get a more detailed understanding about the shock wave structures outside a Laval nozzle and the RR←→MR transition in the dual-solution domain.展开更多
The hollow-pipe perforated breakwater is of low reflection. In this paper the functions of reflection coefficients of both regular and random waves are theoretically derived, based on the concept of linear superimposi...The hollow-pipe perforated breakwater is of low reflection. In this paper the functions of reflection coefficients of both regular and random waves are theoretically derived, based on the concept of linear superimposition of reflected and incident waves and with the total flow rate continuity of integral form instead of the non-continuity of the boundary condition, and based on the concept of linear wave spectrum theory. Comparisons between theoretical results presented here and measurements of model tests show reasonable agreement.展开更多
The reflection of regular and irregular waves from a partially perforated caisson breakwater with a rock-filled core is examined. The present mathematical model is developed by means of the matched eigenfunction metho...The reflection of regular and irregular waves from a partially perforated caisson breakwater with a rock-filled core is examined. The present mathematical model is developed by means of the matched eigenfunction method. Numerical results of the present model are compared with the experimental data of different researchers. Numerical examples are given to examine the effect of rock fill on the reflection coefficient. The differences between regular and irregular waves are also investigated by means of theoretical and experimental results. It is found that the minimum reflection coefficient of irregular waves is larger than that of corresponding regular waves, but the contrary is the case for the maximum reflection coefficient.展开更多
The present work is an analytical study of the influence of geometrical parameters, such as length, thickness and immersion of the plate, on the reflection coefficient of a regular wave for an immersed horizontal plat...The present work is an analytical study of the influence of geometrical parameters, such as length, thickness and immersion of the plate, on the reflection coefficient of a regular wave for an immersed horizontal plate in the presence of a uniform current with the same direction as the propagation of the incident regular wave. This study was performed using the linearized potential theory with the evanescent modes while searching for complex roots to the dispersion equation that are neither pure real nor pure imaginary. The results show that the effects of the immersion and the relative length on the reflection coefficient of the plate are accentuated by the presence of the current, whereas the plate thickness practically does not have an effect if it is relatively small.展开更多
In this paper, by taking into account the thickness of the incident shock as well as the influence of the boundary layer, we point out that even in a regular reflection there should be present a contact discontinuity....In this paper, by taking into account the thickness of the incident shock as well as the influence of the boundary layer, we point out that even in a regular reflection there should be present a contact discontinuity. By using the smallest energy criterion, the inclined angle of this contact discontinuity can be determined for differen incident angle. Then, with this inclined contact discontinuity, together with the law of conservation of mass, the mechanism for the transition from a regular reflection to a Mach reflection or a von Neumann reflection becomes clear. The important roles played by the leftest point in the reflected shock polar are identified.展开更多
文摘In this paper, the hydrodynamic efficiency of a floating breakwater system is experimentally studied by use of physical models. Regular waves with wide ranges of wave heights and periods are tested. The efficiency of the breakwater is presented as a function of the wave transmission, reflection, and energy dissipation coefficients. Different parameters affecting the breakwater efficiency are investigated, e.g. the number of the under connected vertical plates, the length of the mooring wire, and the wave length. It is found that, the transmission coefficient kt decreases with the increase of the relative breakwater width B/L, the number of plates n and the relative wire length l/h, while the reflection coefficient kr takes the opposite trend. Therefore, it is possible to achieve kt values smaller than 0.25 and kr values larger than 0.80 when B/L is larger than 0.25 for the case of l/h-1.5 and n=4. In addition, empirical equations used for estimating the transmission and reflection coefficients are developed by using the dimensionless analysis, regression analysis and measured data and verified by different theoretical and experimental results.
基金supported by the National Natural Science Foundation of China (Grant No. 50779045)the Open Foundation of State Key Laboratory of Hydraulics and Mountain River Engineering (Grant No. 0710)+2 种基金the National Science Foundation for Post-Doctoral Scientists of China (Grant No. 20080440681)the Natural Science Foundation of Tianjin, China (Grant No. 10JCYBJC03700)the Scientific and Technologic Development Foundation of the Higher Education Institutions of Tianjin,China (Grant No. 20080906)
文摘A series of regular and irregular wave experiments are conducted to study the reflective and transmitting performances of quarter circular breakwater （QCB） in comparison with those of semi-circular breakwater （SCB）. Based on regular wave tests, the reflection and transmission characteristics of QCB are analyzed and a few influencing factors are investigated. Then, the wave energy dissipation as wave passing over the breakwater is discussed based on the hydraulic coefficients of QCB and SCB. In irregular wave experiments, the reflection coefficients of QCB and their spectrums are studied. Finally, the comparisons between the experimental results and numerical simulations for QCB under regular and irregular wave conditions are presented.
基金Partially supported by NSF-DMS-0305497 and 0305114.
文摘We establish the existence of a global solution to a regular reflection of a shock hitting a ramp for the pressure gradient system of equations. The set-up of the reflection is the same as that of Mach＇s experiment for the compressible Euler system, i.e., a straight shock hitting a ramp. We assume that the angle of the ramp is close to 90 degrees. The solution has a reflected bow shock wave, called the diffraction of the planar shock at the compressive corner, which is mathematically regarded as a free boundary in the self-similar variable plane. The pressure gradient system of three equations is a subsystem, and an approximation, of the full Euler system, and we offer a couple of derivations.
文摘When the high-pressure gas is exhausted to the vacuum chamber from the nozzle,the underexpanded supersonic jet contained with the Mach disk is generally formed.The eventual purpose of this study is to clarify the unsteady phenomenon of the underexpanded free jet when the back pressure continuously changes with time.The characteristic of the Mach disk has been clarified in consideration of the diameter and position of it by the numerical analysis in this paper.The sonic jet of the exit Mach number Me=1 is assumed and the axisymmetric conservational equation is solved by the TVD method in the numerical calculation.The diameter and position of the Mach disk differs with the results of a steady jet and the influence on the continuously changing of the back pressure is evidenced from the comparison with the case of steady supersonic jet.
文摘Using a discretized finite difference method, a numerical model was developed to study the interaction of regular waves with a perforated breakwater. Considering a non-viscous, non-rotational fluid, the governing equations of Laplacian velocity potential were developed, and specific conditions for every single boundary were defined. The final developed model was evaluated based on an existing experimental result. The evaluated model was used to simulate the condition for various wave periods from 0.6 to 2 s. The reflection coefficient and transmission coefficient of waves were examined with different breakwater porosities, wave steepnesses, and angular frequencies. The results show that the developed model can suitably present the effect of the structural and hydraulic parameters on the reflection and transmission coefficients. It was also found that with the increase in wave steepness, the reflection coefficient increased logarithmically, while the transmission coefficient decreased logarithmically.
基金supported by the National Natural Science Foundation of China (No. 10702009)
文摘When the pressure ratio increases from the perfectly expanded condition to the third limited condition in which a normal shock is located on the exit plane, shock wave configurations outside the nozzle can be further assorted as no shock wave on the perfectly expanded condition, weak oblique shock reflection in the regular reflection （RR） pressure ratio condition, shock reflection hysteresis in the dual-solution domain of pressure ratio condition, Mach disk configurations in the Mach reflection （MR） pressure ratio condition, the strong oblique shock wave configurations in the corresponding condition, and a normal shock forms on the exit plane in the third limited con- dition. Every critical pressure ratio, especially under regular reflection and Mach reflection pressure ratio conditions, is deduced in the paper according to shock wave reflection theory. A hysteresis phenomenon is also theoretically possible in the dual-solution domain. For a planar Laval nozzle with the cross-section area ratio being 5, different critical pressure ratios are counted in these con- ditions, and numerical simulations are made to demonstrate these various shock wave configurations outside the nozzle. Theoretical analysis and numerical simulations are made to get a more detailed understanding about the shock wave structures outside a Laval nozzle and the RR←→MR transition in the dual-solution domain.
文摘The hollow-pipe perforated breakwater is of low reflection. In this paper the functions of reflection coefficients of both regular and random waves are theoretically derived, based on the concept of linear superimposition of reflected and incident waves and with the total flow rate continuity of integral form instead of the non-continuity of the boundary condition, and based on the concept of linear wave spectrum theory. Comparisons between theoretical results presented here and measurements of model tests show reasonable agreement.
文摘The reflection of regular and irregular waves from a partially perforated caisson breakwater with a rock-filled core is examined. The present mathematical model is developed by means of the matched eigenfunction method. Numerical results of the present model are compared with the experimental data of different researchers. Numerical examples are given to examine the effect of rock fill on the reflection coefficient. The differences between regular and irregular waves are also investigated by means of theoretical and experimental results. It is found that the minimum reflection coefficient of irregular waves is larger than that of corresponding regular waves, but the contrary is the case for the maximum reflection coefficient.
文摘The present work is an analytical study of the influence of geometrical parameters, such as length, thickness and immersion of the plate, on the reflection coefficient of a regular wave for an immersed horizontal plate in the presence of a uniform current with the same direction as the propagation of the incident regular wave. This study was performed using the linearized potential theory with the evanescent modes while searching for complex roots to the dispersion equation that are neither pure real nor pure imaginary. The results show that the effects of the immersion and the relative length on the reflection coefficient of the plate are accentuated by the presence of the current, whereas the plate thickness practically does not have an effect if it is relatively small.
基金supported by the NNSF of China(11271323,91330105)the Zhejiang Provincial Natural Science Foundation of China(LZ13A010002)supported by a GRF grant(City U 11303015)from the Research Grants Council of Hong Kong SAR,China
文摘In this paper, by taking into account the thickness of the incident shock as well as the influence of the boundary layer, we point out that even in a regular reflection there should be present a contact discontinuity. By using the smallest energy criterion, the inclined angle of this contact discontinuity can be determined for differen incident angle. Then, with this inclined contact discontinuity, together with the law of conservation of mass, the mechanism for the transition from a regular reflection to a Mach reflection or a von Neumann reflection becomes clear. The important roles played by the leftest point in the reflected shock polar are identified.
