【作者】 吴静萍；

【导师】 王仁康； 邹早建；

【作者基本信息】 武汉理工大学 ， 流体力学， 2004， 博士

【摘要】 对船舶及海洋结构物与波浪、流的相互作用的研究，越来越多地采用数值方法，即数值波浪水池(NWT)。本文应用势流理论和频域方法研究了三维浮体在深水域波浪中航行时的非线性绕射问题，该问题包括非线性兴波问题和非线性绕射问题。 该类流固相互作用的非线性水波流动问题，由于自由面条件的非线性而难于求解，常用各种方法近似模拟。本文应用Stokes非线性波理论的方法，将流场速度势和波面升高摄动展开，推导了一阶、二阶兴波速度势和绕射速度势的自由面条件，并且绕射速度势的自由面条件中包含非线性的兴波速度势。文中，一阶绕射速度势的辐射条件采用了与定常流动完全相同的自由面网格错位的数值方法，并推广应用到二阶绕射速度势。 对非线性流动的数值计算，目前广泛采用时域方法，但时域方法计算量大、存储量大。而频域方法适宜于求解线性问题，其对二维、三维一阶线性问题的模拟具有足够的精度，已广泛应用于实际工程。本文的一阶、二阶绕射速度势的定解问题是线性的，假设扰动稳定、具有周期性，采用频域方法求解，大大减少了计算量。 势流问题大量采用边界元方法数值求解。本文采用非均匀有理B样条(NURBS)方法精确表达三维物体表面，物面及物面函数的高阶导数连续；采用非奇异方法在物体内部和自由面上方布置Rankine源，不存在积分方程的奇异性，无不规则频率现象，并且速度势在物面的导数可以直接函数求导。 在本文的数值计算中，影响计算结果收敛的主要因素有：非奇异源的物面内潜深度、自由面上的提升高度、自由面的计算范围以及自由面和物面边界上配置点的间距(或数量)。本文选取足够的自由面计算范围和边界配置点数量，讨论了物面内潜深度和自由面上提升高度对计算结果收敛的影响，并建议了内潜距离的计算表达式，获得了一致收敛的数值解。 本文研究了潜水椭球和Wigley船型的兴波问题和绕射问题，计算了非线性的兴波阻力系数、纵向一阶波浪扰动力和二阶倍频波浪扰动力，以及兴波武汉理工大学博士学位论文波形和绕射波形。并将兴波阻力系数、一阶波浪扰动力的计算结果与试验结果和他人的计算结果进行了比较，吻合程度较好。文中还就流动的非线性对物体的波浪扰动力和自由面波形的影响进行了讨论。 本文的关键是通过求解二阶绕射速度势获得三维移动物体的二阶倍频波浪力。通过实际编程计算，证明了本文所采用的理论方法、数值方法和所编程序是正确有效的。本文虽然以航行物体为研究对象，但是同样适用于波浪和流共同作用于固定结构物的问题。关键词:非线性绕射，倍频波浪力，非线性兴波，非奇异方法，频域，边界元方法，Rankine源更多还原

【Abstract】 There are more and more applications of numerical method, i.e. Numerical Wave Tank (NWT), to research the interaction of ship and offshore structure with wave and current. In this paper, the nonlinear diffraction problem is studied with potential flow theory in frequency domain for three-dimensional floating body sailing in waves on deep water. This problem includes nonlinear diffraction problem and nonlinear wave making problem.It is harder to solve accurately such nonlinear water wave problem because of the nonlinear free-surface condition; various kinds of approximations are developed. In this paper, by adopting the Stokes nonlinear wave theory of deep water, the total flow velocity potential and wave elevation are decomposed into first-order and higher order ones, and the nonlinear free-surface condition is expanded by Stokes perturbation technique. The free-surface condition of diffraction problem contains nonlinear wave making velocity potential. The radiation condition of the first-order diffraction problem is dealt with by the numerical method just in the same way as that is applied in steady wave making problem, and the method is extended to the second-order diffraction problem.Time domain is the most popular method to solve nonlinear wave flow. But it takes both computer time and memory. Frequency domain is suitable for computing linear problem in common sense, and it is widely used and works well in the first-order linear problem. In this paper, the frequency domain is developed to solve the first and second diffraction problems by assuming the perturbation is steady and periodic, and the need of computer power decreases largely.Boundary element method is the most widely used method for potential flow. In this paper, NURBS method is used to describe the body surface accurately, the body surface and its differentiation are continuous; the de-singularized method isused to numerically compute the problems, so there is no singularity, no irregular frequency. And the differentiation of potential on body surface can be carried out directly.In this paper, the major factors which have effects on the numerical convergence includ the inner distance of the sources submersed into the body surface, the distance moved upward above the mean free-surface, the computing range of free surface, and the collocation point interval (or number). With enough free-surface range and collocation point number, this paper discusses the effects of the two kinds of distances on the numerical convergence, proposes the expressions for the inner distance, and has obtained consistent and convergence results.In this paper, choosing submerged spheroids and Wigley hulls as computing models, the computed wave resistance and first-order wave exciting force are in good agreement with the other published results. The second-order wave exciting force, nonlinear wave making and nonlinear diffraction wave contour are calculated also. The effect of the nonlinearity on total wave exciting force and wave contour is discussed.The key of this paper is the solution of the second-order double-frequency wave exciting force for a floating body sailing in waves by solving second-order diffraction potential. All computed results show the theory and numerical methods in this paper are correct and valid. Although this paper deals with a floating body all methods can be used to the fixed offshore structures in waves and current.更多还原