【作者】 耿宝磊；

【导师】 滕斌；

【作者基本信息】 大连理工大学 ， 港口、海岸及近海工程， 2010， 博士

【摘要】 本文采用高阶边界元方法,在时域内首先研究了绕(辐)射场中具有大尺度结构物和小尺度杆件的复合海洋结构上小尺度杆件的波浪荷载,重点研究了我国南海百年一遇灾害海洋环境下一座Truss Spar平台和一座半潜平台的水动力特性。本文以三维Laplace方程为基本控制方程建立了线性波浪与任意三维结构物作用的数学模型。通过泰勒级数展开使自由水面边界条件在平均静水面上满足,物面边界条件在平均物面上满足,从而将计算域限制在一个不随时间变化的固定区域内。利用摄动展开并分离入射波浪和散射波浪,建立了线性的边值问题。引入Rankine源和它关于海底的像为格林函数,并利用格林第二定理,建立了关于波浪场中任意点速度势的边界积分方程。通过一系列复杂的变换,将积分方程离散成以物面单元节点速度势和水面单元节点速度势导数为未知量的矩阵方程。利用三角极坐标变换处理数值计算中的奇异积分问题；固角系数通过采用直接计算得到,保证了各种情况下的计算精度；将物体的对称性应用到求解过程中,从而简化了矩阵方程,大大节约了计算量和计算时间。在时域计算过程中,利用四阶龙格-库塔法对自由表面上的速度势和瞬时波面进行积分更新；对于物体的运动方程,同样利用四阶龙格-库塔法进行迭代求解。在初始时刻加入缓冲函数；在计算域的边界布置阻尼层,保证了在一个有限的时间域和空间域内得到稳定的计算结果。本文首先研究了绕(辐)射场中具有大尺度结构物和小尺度杆件的复合海洋结构上小尺度杆件的波浪荷载,给出了绕射势作用下水质点速度和加速度的计算公式,并与解析解进行了对比。对于给定的结构,计算分析了规则波和畸形波作用下小尺度桩柱上波浪荷载的特性,并进一步研究了大尺度结构尺寸变化和小尺度桩柱在绕射场中位置的变化对小尺度桩柱上波浪荷载的影响。最后对运动物体上的小尺度杆件所受的波浪荷载进行了理论推导。本文重点研究了我国南海百年一遇灾害海洋环境下一座Truss Spar平台和一座半潜平台的水动力特性。通过计算阻尼矩阵研究了阻尼对海洋平台一阶运动响应的影响,得到了平台各自不同位移方向的固有周期。分别对四种荷载组合下Truss Spar平台和半潜平台的运动响应进行了时域模拟,得到了各种荷载组合下两座平台的波浪力、位移和缆绳张力的时间历程曲线,并进行了分析。计算得到两座平台所受风荷载和流荷载,以及在风、流作用下平台的平衡位置,并分析了阻尼矩阵对计算过程的影响。文中还给出了波浪作用下Truss Spar平台波浪爬高和半潜平台最小气隙的计算方法,并分别画出了规则波和不规则波作用下水面的变化及波高的分布。更多还原

【Abstract】 Based on the high-order boundary element method, the wave force on small-scale members of a composite structure was firstly investigated in diffraction field in time domain. The study is mainly focused on the hydrodynamic characteristics of a Truss Spar and a semi-submersible platform in the South China Sea with 100-year marine environmental disaster.By taking the 3D Laplace equation as the basic governing equation, a mathematical model with respect to the interaction between linear waves and arbitrary 3D structures was founded. The Taylor series expansion was used to satisfy the free surface boundary condition on the mean static water and the solid-wall boundary conditions on the average body surfaces, respectively. Therefore, the computational domain can be restricted to a fixed time-invariant scope. With the use of perturbation expansion and the seperation of the incident and diffraction (scattering) waves, a linear boundary value problem was set up. By introducing the Rankine source and its image on the sea bottom as the Green function, a boundary integral equation for the velocity potential of an arbitrary point in the wave field was obtained based on the second Green identity.Through a series of complicated transformation, the integral equation was discretized into matrix equations, with the nodal potential of body elements and the nodal normal derivative of velocity potential of the water surface elements as the unknowns. The singular integral problems emerged in calculations were solved through triangular polar coordinate transformation; the solid angle coefficient was acquired through direct calculation, which guaranteed the calculation precision in different conditions. With the symmetry applied to the solution process, the matrix equations were simplified, and the amount of calculation was reduced greatly.In the time-domain calculation, the fourth-order Runge-Kutta method was adopted to update the velocity potential and the instantaneous wave elevation on the free surface. As to the motion equations for objects, the fourth-order Runge-Kutta method was employed again for iterative solution. A ramp function was added at the beginning of calculation. A damping layer was arranged at the boundaries of the computational domain to ensure that steady calculation results can be obtained within a finite time and space domain. Formula for calculating the wave forces on the small-scale members in the diffraction field were firstly derived. The water-particle velocities produced by the diffracting waves were solved using integral equations, and the acceleration was obtained based on the time difference. For some specific examples, the accuracy of the velocity and the acceleration obtained with this method was verified by comparison with the analytical solutions. For a given structure, the characteristics of the wave load on the small-scale members under the action of regular waves and freak waves were analyzed. Then the influence of the size of an upper large-scale structure on the wave load on a small-scale structure was investigated. Finally, the wave load on the medium small-scale member bars at different positions in the diffraction field was analyzed. For oblique members on moving body, the solution procedure was deduced in detail.The hydrodynamic characteristics of a Truss Spar and a semi-submersible platform in South China Sea with 100-years marine environmental disasters were investigated in emphasis. The viscosity damping effect on first order motion respose was studied by calculating the damping matrix, and the different motion nature period of each platform was obtained by analzing the displacement-time curve. Time domain simulation was carried out for each platform reponse under four kinds of loading combinations, and the time history of wave loadings, replacement, and mooring tension forces were get and analyzed, respectively. The wind and current loads on each platform were calculated and then the equilibrium positions under these loads were obtained. The wave run-up for Truss Spar and minimum air-gap for semi-submersible platform were given under waves. The changing of the wave surface and the wave height distribution for regular waves and irregular waves were described, respectively.更多还原