半无限延展弹性冰层限制的冰区航道内船舶与水波共振机理研究

As the commercial shipping routes through Arctic region become viable, there has been increased interest in assessment of the hydrodynamic performance of a ship sailing in polar regions. Different with open water or water channel confined between two solid walls, the water channel confined between two semi-infinite ice sheets has a series of its natural frequencies in addition to that of the ship itself. Within the typical wave periods, there exists many resonance frequencies at which large amplitude motions would happen. However, the numerical analysis methods developed previously are still limited to solve the 2D simplified models, and the mechanism for the complicated resonance phenomenon is not clear until now. Based on the above reasons, the present study intends to establish a more accurate 3D multi-domain hybrid method in frequency domain. The strategy is to divide the total fluid domain into three sub-regions. On the one hand, the velocity potentials are expanded in form of eigenfunctions or expressed in integral form with a proper Green function in the two-exterior ice covered regions. Thus, the complicated ice covered upper surface conditions are to be satisfied analytically. On the other hand, the potentials are expanded in form of Fourier series on the artificial interfaces. Then, the unknown coefficients as well as potentials will be found together by the Galerkin method based on the continuous conditions. Finally, laboratory experiment using unbreakable ice sheet will be carried out to verify the accuracy of the proposed method; Through systematic study, the effects of environment parameters on motion characters will be analyzed, and the mechanical mechanism behind the complicated resonance phenomenon will be further studied, which aims to provide an efficient analysis method for the assessment of the seakeeping performance and wave load of the Arctic commercial ship.

冰区航道内船舶水动力性能分析是极地运输船舶设计的重要课题之一。两侧由半无限延展弹性冰层限制的冰区航道存在系列固有频率，行驶于其中的船舶会与水波在多个频率下发生复杂共振现象，对人员和财产构成巨大威胁。目前对该问题的研究尚不能考虑流场三维效应，对航道内船舶与水波复杂共振现象的力学分析也十分匮乏。鉴于此，本研究拟基于已有二维模型，发展更为准确的三维多流体域匹配分析方法。一方面，在两侧冰层覆盖流域，推导速度势的本征函数级数展开式和冰面格林函数边界积分式，解析满足半无限延展冰层覆盖水面条件与相应的远方辐射条件；另一方面，推导流域分界面上速度势的二重广义傅立叶级数展开式，建立积分意义下的速度势精确匹配模型。利用非冻结不可破碎模型冰，设计物理模型实验，验证分析方法的有效性，在此基础上，精细化研究冰区航道内船舶与水波的共振机理，旨在为极地运输船舶的耐波性设计和波浪载荷评估提供有效的分析方法和基础理论支撑。

半无限延展弹性冰层限制的冰区航道存在系列流体共振频率，航道内的船舶水动力随波浪频率变化存在系列极值。在典型波浪周期内，船舶与水波可能在多个频率下发生复杂的共振现象，严重威胁船舶的舒适性和安全性。本项目以极地工程领域中船舶耐波性设计和环境载荷评估为工程背景，通过建立三维多流体域匹配分析方法，探明冰区航道内船舶的水动力特征，揭示船舶与水波共振运动的力学机理，并形成极地船舶冰水载荷数值预报技术。.项目研究中，基于垂向特征函数展开式，解析满足了含高阶混合偏导数的复杂冰面条件；通过沿冰区航道方向的傅里叶积分变换，将无限长物理平面匹配问题转化成了每个傅里叶参数下的横剖面匹配问题；在不同横剖面子域内应用格林定理，实现了不同子域未知量的联合匹配求解，进而得出冰区航道内脉动点源扰动流场的基本解，即格林函数。研究发现，当自由表面波波数大于弯曲重力波波数时，冰区航道内可能存在一系列捕获波，其沿航道前后呈无衰减传播，而向航道两侧呈指数衰减传播。此外，捕获波子波随波浪频率的增加而增多。.利用边界单元法，结合冰区航道格林函数，建立了三维数值程序。研究发现，冰区航道内船舶水动力振荡特性随航道宽度和船体偏离航道中心距离的增加而加剧。当航道内存在多浮体时，捕获波会加强多浮体之间的耦合效应，并诱发形成更大的流体载荷和波面升高。特别是，受冰区航道捕获波影响，即使浮体间距很远，多浮体之间的耦合效应仍十分明显。对于冰区航道内单个细长体，二维模型可以给出合理的预报结果，但是对于多浮体耦合作用问题，简化模型无法考虑冰区航道流场的捕获波效应。.研究结果为冰区航道内极地船舶的水动力性能评估提供了有效的分析方法和基础理论支撑，对研究人员认识和理解冰区航道内船舶与水波的流体共振现象和载荷振荡变化特征具有重要的科学意义，所建立的三维多流体域匹配模型，也将为类似非一致边界条件下流体动力问题的研究提供建模参考。