斜坡式防波堤越浪过程的SPH模拟
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摘要
本文应用基于CSPM法和黎曼解修正的SPH方法建立了主动吸收式二维数值波浪水槽,研究了波浪沿斜坡堤爬坡和越浪过程的水动力特性。
首先,对斜坡堤越浪的研究情况及SPH在水动力学方面的应用情况作了简要的回顾。
然后,详细介绍了SPH方法的基本方程,即函数近似和粒子近似方程,并在此基础上对基本的控制方程进行了粒子离散,同时介绍了相关的实现技术,如边界条件、搜索方法和时间积分等。接着研究了孤立波在不可渗斜坡堤上的爬坡和越浪过程波面的空间分布及在各个测点历时变化,通过计算结果和试验结果的对比来验证本文建立的数学模型。
最后,对规则波沿可渗透斜坡爬坡和越浪进行了研究。将可渗透斜坡按多孔介质处理,即将自由液面以下的可渗透层离散成流体粒子,求解的是空间平均流动。对渗透层外的流体求解N-S方程,在渗透层内通过将附加外力项加入动量方程来考虑多孔介质对流体的影响。首先研究了水槽内各个测点自由液面的变化和波浪沿斜坡爬坡和越浪过程中可渗透斜坡堤内的流场和压力分布情况,然后在不同周期、波高、斜坡坡度、孔隙率和平均粒径的情况下研究了越浪量的变化。结果表明：采用修正后的SPH方法所建立的模型计算得到的波面变化情况和试验结果有较好的吻合；在本文数值模型计算范围内,周期、波高和斜坡坡度对越浪量的影响最大,越浪量随周期和波高的增加而增加,随斜坡坡度的增加而减少；孔隙率对越浪量的影响最小,在周期较小的情况孔隙率为0.4时越浪量有最小值,但与其他孔隙率情况下的越浪量的差值微小,当周期为2s的时越浪量不再随孔隙率变化；平均粒径对越浪量的影响主要体现在小粒径范围内,平均粒径在10mm到25mm的范围内越浪量随粒径的增加明显减少,平均粒径大于25mm以后越浪量变化很小。
An 2D active absorbing wave flume was built based on the corrected SPH method by CSPM and Reimann solver to study the water dynamics of wave run-up and overtopping on sloping breakwaters.
Firstly, the research of wave overtopping on breakwaters and the applications of SPH in hydrodynamics were briefly reviewed.
Secondly, the basic equations, namely function approximation and particles approximation, were introduced in detail. The relative implementation technologies of SPH, such as boundary conditions, particles search algorithm and time integral, were also discussed. and then, the change of free surfaces profiles at different points when solitary wave run-up and overtopping on impermeable sloping breakwater were studied to validate the numerical models used in this paper by comparing SPH results and experiment data.
Finally, regular wave run-up and overtopping on permeable sloping breakwaters were studied. The slope was dealt as porous media, namely, the permeable layer under the water surface was filled with particles. The spatial average flow was solved. The SPH model solves NS equations for the flows outside the porous media and the NS type equations for the flows inside the porous media. The presence of porous media is considered by including additional friction into the equations. Water surface elevations at different points and pressure fields in the porous media were both studied. And then the relations between overtopping mass and different periods, different wave heights, different gradient and diameters were studied. The results show that:the wave surfaces predicted by the model based corrected SPH is in good agreement with experiment data; in the range of numerical model, overtopping mass changed greatly with wave periods, wave height and gradient. the overtopping mass increases when wave height and period increase and decreases when gradient increases; porosity has least influence on overtopping mass, the overtopping mass has a least value when porosity is 0.4 in small period, but the difference is minor, when the period is 2 second, overtopping mass was no change with porosity anymore; when the size of diameter increases from 10mm to 25mm, overtopping mass decreases evidently, when the size of the diameter is greater than 25mm, overtopping mass changes little.
首先,对斜坡堤越浪的研究情况及SPH在水动力学方面的应用情况作了简要的回顾。
然后,详细介绍了SPH方法的基本方程,即函数近似和粒子近似方程,并在此基础上对基本的控制方程进行了粒子离散,同时介绍了相关的实现技术,如边界条件、搜索方法和时间积分等。接着研究了孤立波在不可渗斜坡堤上的爬坡和越浪过程波面的空间分布及在各个测点历时变化,通过计算结果和试验结果的对比来验证本文建立的数学模型。
最后,对规则波沿可渗透斜坡爬坡和越浪进行了研究。将可渗透斜坡按多孔介质处理,即将自由液面以下的可渗透层离散成流体粒子,求解的是空间平均流动。对渗透层外的流体求解N-S方程,在渗透层内通过将附加外力项加入动量方程来考虑多孔介质对流体的影响。首先研究了水槽内各个测点自由液面的变化和波浪沿斜坡爬坡和越浪过程中可渗透斜坡堤内的流场和压力分布情况,然后在不同周期、波高、斜坡坡度、孔隙率和平均粒径的情况下研究了越浪量的变化。结果表明：采用修正后的SPH方法所建立的模型计算得到的波面变化情况和试验结果有较好的吻合；在本文数值模型计算范围内,周期、波高和斜坡坡度对越浪量的影响最大,越浪量随周期和波高的增加而增加,随斜坡坡度的增加而减少；孔隙率对越浪量的影响最小,在周期较小的情况孔隙率为0.4时越浪量有最小值,但与其他孔隙率情况下的越浪量的差值微小,当周期为2s的时越浪量不再随孔隙率变化；平均粒径对越浪量的影响主要体现在小粒径范围内,平均粒径在10mm到25mm的范围内越浪量随粒径的增加明显减少,平均粒径大于25mm以后越浪量变化很小。
An 2D active absorbing wave flume was built based on the corrected SPH method by CSPM and Reimann solver to study the water dynamics of wave run-up and overtopping on sloping breakwaters.
Firstly, the research of wave overtopping on breakwaters and the applications of SPH in hydrodynamics were briefly reviewed.
Secondly, the basic equations, namely function approximation and particles approximation, were introduced in detail. The relative implementation technologies of SPH, such as boundary conditions, particles search algorithm and time integral, were also discussed. and then, the change of free surfaces profiles at different points when solitary wave run-up and overtopping on impermeable sloping breakwater were studied to validate the numerical models used in this paper by comparing SPH results and experiment data.
Finally, regular wave run-up and overtopping on permeable sloping breakwaters were studied. The slope was dealt as porous media, namely, the permeable layer under the water surface was filled with particles. The spatial average flow was solved. The SPH model solves NS equations for the flows outside the porous media and the NS type equations for the flows inside the porous media. The presence of porous media is considered by including additional friction into the equations. Water surface elevations at different points and pressure fields in the porous media were both studied. And then the relations between overtopping mass and different periods, different wave heights, different gradient and diameters were studied. The results show that:the wave surfaces predicted by the model based corrected SPH is in good agreement with experiment data; in the range of numerical model, overtopping mass changed greatly with wave periods, wave height and gradient. the overtopping mass increases when wave height and period increase and decreases when gradient increases; porosity has least influence on overtopping mass, the overtopping mass has a least value when porosity is 0.4 in small period, but the difference is minor, when the period is 2 second, overtopping mass was no change with porosity anymore; when the size of diameter increases from 10mm to 25mm, overtopping mass decreases evidently, when the size of the diameter is greater than 25mm, overtopping mass changes little.
引文
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