波浪中多物体耦合作用简单高效计算方法
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摘要
分析港内船舶在波浪中运动对保障船舶安全性和设计有着十分重要的意义。对船舶和采油平台一类的单个结构物的计算可以采用通常的三维源汇分布法。但对于多个物体之间相互作用的计算,这一方法计算量比较大。因为这一方法需要大量的面源,尤其对于高频的情况。其计算量会随着物体的尺度和数量增大而增加。针对波浪中多物体的情况,这里需要一个快速的计算方法。Lean等提出的一个方法就适用于这类问题。该方法是将船体横剖面用具有相等面积和相同吃水的等效矩形代替,将流场划分为船底与水底之间的内场和船侧面之外的外场。对内场的速度势由解析解表达,对外场,在自由水面处物体周线上分布源汇,其速度势可沿水深作傅立叶级数展开。内外场速度势可以通过内外场匹配条件来求出。该方法仅对物体横剖面作近似处理,这使得该方法仅适用于细长型船体。
本文扩展了Lean等的方法,对物体的横剖面和纵剖面同时作近似处理,用具有相等面积和相同吃水的等效矩形代替。这样船体底部横向流场和纵向流场就可以同时被考虑。由于本方法对物体同时采用横剖和纵剖,所以本方法不仅适用于细长型船体,也可适用于箱型船等具有较肥大船艏船艉的船型。基于上述计算方法给出了船体二阶波浪力的计算方法。同时在本文研究中,将计算船体方法与直立柱体的求解相结合,使得该方法扩展为多船多柱体相互作用问题的求解,从而构成了这类计算问题的一个简单高效的计算方法。通过应用本方法做了以下工作：
(1)采用本方法对多船和直立码头(在计算中采用细长截面矩形墩)相互作用的情况进行了计算,分析了单船、两条船及三条船和码头间相互作用和船体的运动问题。并且也计算了码头为多墩柱离岸码头时船与多墩柱码头的相互作用；
(2)把本文的计算方法应用于有船体存在的港内波浪计算,分析了有船和无船时港内波浪的分布特征,对港内波浪和船体的相互作用进行研究,给出了船体的水动力系数、波浪力和运动的特征；
(3)把本方法在频域内计算的结果应用于船舶运动时域模型,建立了基于本方法的系泊浮体时域运动方程。采用该时域模型模拟一系泊浮式养鱼池在随机波浪作用下的受力和运动,给出了系缆张力、一阶波浪力和二阶波浪力及其浮体运动响应。
The analysis of hydrodynamic problems is an important subject of ship security and design. The hydrodynamics of a single structure in waves, such as a ship or a production platform, are usually calculated by the three-dimensional source-sink distribution method. But difficulties in actual computations may arise for calculations of the interaction of multiple bodies, since a lot of source panels are needed for this kind of numerical calculations, especially for a high wave frequency case. The computation work increases with the increase of size and number of structures. So for multiple-bodies case, a simple and efficient method is called for. The method proposed by Lean et al is a possible choice for such a purpose. This method approximates a ship cross section by a rectangle with the same area of the original ship section, and divides the flow field into inner domain below the ship bottom and the outer domain beside ship hull. The inner-domain velocity potential is given by a simple analytic solution, and the outer-domain velocity potential, given by a source-sink distribution along the contour of ship water area, is expanded over water depth as a Fourier series. The two velocity potentials are matched at the interface of two domains by matching condition. This method only solves the slender ship due to approximate a ship cross section.
The present study extends Lean's method to approximate a ship cross section and longitudinal section by a rectangle with the same area of the original ship section. So the flow fields under the ship can be considerd in cross direction and longitudinal direction. The method solves not only the slender ship but also the fat ship. Based on the method mentioned above, the paper provide the method for calculating the second order wave force of the ship. At the same time, the problem for piers is treated as the case with the gap between ship bottom and seabed being zero. The above simple method can yield a simple and efficient calculation method for the coupling of multiple ships and piers in waves. The paper has done the following jobs by using the method:
(1) The paper calculates the case of many ships against vertical quay(a long rectangle pier adopted in calculation), analyses the interaction of the case of one ship and pier, the case of two ships and pier and the case of three ships and pier, and presents the ship responses. As the quay is made up of multiple piers, the paper calculates the interaction between the ship and quay;
(2) The method has been used in the case of many ships in the harbor. The paper gives distribution characters of waves in the harbor including the presence of the ship in the harbor and nothing in the harbor, and calculates the wave forces and ship responses;
(3) Frequency domain results using the method are applied in the model of time domain, so that the motion equations are founded in the time domain. In the same time, the dynamic analysis of the tank mooring system is conducted using the mathematical models to evaluate the force and response of the tank in a random sea sate. The results include the mooring line forces, the first order wave forces, the second order wave forces and the motions of the tank.
本文扩展了Lean等的方法,对物体的横剖面和纵剖面同时作近似处理,用具有相等面积和相同吃水的等效矩形代替。这样船体底部横向流场和纵向流场就可以同时被考虑。由于本方法对物体同时采用横剖和纵剖,所以本方法不仅适用于细长型船体,也可适用于箱型船等具有较肥大船艏船艉的船型。基于上述计算方法给出了船体二阶波浪力的计算方法。同时在本文研究中,将计算船体方法与直立柱体的求解相结合,使得该方法扩展为多船多柱体相互作用问题的求解,从而构成了这类计算问题的一个简单高效的计算方法。通过应用本方法做了以下工作：
(1)采用本方法对多船和直立码头(在计算中采用细长截面矩形墩)相互作用的情况进行了计算,分析了单船、两条船及三条船和码头间相互作用和船体的运动问题。并且也计算了码头为多墩柱离岸码头时船与多墩柱码头的相互作用；
(2)把本文的计算方法应用于有船体存在的港内波浪计算,分析了有船和无船时港内波浪的分布特征,对港内波浪和船体的相互作用进行研究,给出了船体的水动力系数、波浪力和运动的特征；
(3)把本方法在频域内计算的结果应用于船舶运动时域模型,建立了基于本方法的系泊浮体时域运动方程。采用该时域模型模拟一系泊浮式养鱼池在随机波浪作用下的受力和运动,给出了系缆张力、一阶波浪力和二阶波浪力及其浮体运动响应。
The analysis of hydrodynamic problems is an important subject of ship security and design. The hydrodynamics of a single structure in waves, such as a ship or a production platform, are usually calculated by the three-dimensional source-sink distribution method. But difficulties in actual computations may arise for calculations of the interaction of multiple bodies, since a lot of source panels are needed for this kind of numerical calculations, especially for a high wave frequency case. The computation work increases with the increase of size and number of structures. So for multiple-bodies case, a simple and efficient method is called for. The method proposed by Lean et al is a possible choice for such a purpose. This method approximates a ship cross section by a rectangle with the same area of the original ship section, and divides the flow field into inner domain below the ship bottom and the outer domain beside ship hull. The inner-domain velocity potential is given by a simple analytic solution, and the outer-domain velocity potential, given by a source-sink distribution along the contour of ship water area, is expanded over water depth as a Fourier series. The two velocity potentials are matched at the interface of two domains by matching condition. This method only solves the slender ship due to approximate a ship cross section.
The present study extends Lean's method to approximate a ship cross section and longitudinal section by a rectangle with the same area of the original ship section. So the flow fields under the ship can be considerd in cross direction and longitudinal direction. The method solves not only the slender ship but also the fat ship. Based on the method mentioned above, the paper provide the method for calculating the second order wave force of the ship. At the same time, the problem for piers is treated as the case with the gap between ship bottom and seabed being zero. The above simple method can yield a simple and efficient calculation method for the coupling of multiple ships and piers in waves. The paper has done the following jobs by using the method:
(1) The paper calculates the case of many ships against vertical quay(a long rectangle pier adopted in calculation), analyses the interaction of the case of one ship and pier, the case of two ships and pier and the case of three ships and pier, and presents the ship responses. As the quay is made up of multiple piers, the paper calculates the interaction between the ship and quay;
(2) The method has been used in the case of many ships in the harbor. The paper gives distribution characters of waves in the harbor including the presence of the ship in the harbor and nothing in the harbor, and calculates the wave forces and ship responses;
(3) Frequency domain results using the method are applied in the model of time domain, so that the motion equations are founded in the time domain. In the same time, the dynamic analysis of the tank mooring system is conducted using the mathematical models to evaluate the force and response of the tank in a random sea sate. The results include the mooring line forces, the first order wave forces, the second order wave forces and the motions of the tank.
引文
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