Pertubational study on the flow field around a planing plate with splay phenomena

为了解决滑行板在持续和自由运行状态下未知湿面的确定问题，本文研究了三种情况下的摄动近似：1)三维滑行板的高深宽比近似推导了确定滑行板湿润长度分布的非线性积分方程。该解决方案获得了对性能的静态稳定性和支撑平板暴露在静止水面上的极限高度的洞察。所得到的湿表面构型很好地描绘了喷雾根线穿越硬中国的行为，但不幸的是，它与实验结果吻合得较宽。2)重力作用下二维滑板的高弗劳德数近似将未知边界问题归结为一个关于弗劳德数Fn的特征值问题。3)三维滑行板的低展宽比近似在船头近场找到一个与局部解匹配的整体解，其中水面变形为曲率未知的抛物线柱体。为了考虑滑行面后部产生的位移效应，求解了描述整场特性的Bollay积分方程，但求解了匹配条件。还存在一些有待解决的问题。

It is intended to solve a problem to determine the unknown wetted surface of planing plates in sustained and free-running conditions.Three cases of the pertubational approximation are studied as followings :1) High aspect ratio approximation of 3D planing plateA non-linear integral equation to determine the wetted length distribution is derived. The solution gains as insight into static stability in performance and the limit height to sustain the plate in exposure above the still water surface. The obtained configuration of wetted surface draws well the behavior of the spray root line crossing the hard chine, however it is unfortunately rather wide to coincide with the experimental one. Too wide planing plate can not freely run.2) High Froude number approximation of 2D planing plate in gravitationNon-dimensional formulation by using the wetted length as a length scale reduce the unknown boundary problem to an eigenvalue problem with respect to Froude number Fn. Two wetted lengths of the solution of the eigenvalue equation exist to the same rise in exposure above the still water surface, however, the shorter one may be unrealizable because of losing static stability.3) Low aspect ratio approximation of 3D planing plateIt is intended to find a global solution matching with the local solution in the bow near field where the water surface deformed as a parabolic cylinder with unknown curvature. Bollay's integral equation expressing the whole field characteristics but the matching condition is solved for taking account of the displacement effect generating by the aft part of planing surface. Some problems to be solved are left.