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

旨在解决刨花板在持续自由运行条件下未知湿面确定问题。研究了三种情况下的微扰近似：1)三维平面的高纵横比近似，推导了确定湿长分布的非线性积分方程。该解决方案获得了性能的静态稳定性和极限高度，以维持板在静止水面以上的暴露。所得的湿表面形态较好地反映了喷淋根线穿过硬面的行为，但与实验结果的吻合较宽。太宽的刨板不能自由运行。2)二维平面平面重力无量纲公式中以湿长度为长度尺度的高弗劳德数近似，将未知边界问题简化为关于弗劳德数Fn的特征值问题。对于相同的水面暴露上升，特征值方程的解存在两个湿润长度，但较短的长度可能由于失去静稳定性而无法实现。3)三维平面低纵横比逼近在水面变形为曲率未知的抛物线圆柱体的船首近场中，寻找与局部解匹配的全局解。波莱积分方程表达了整个场的特性，但考虑了刨面尾部产生的位移效应，求解了匹配条件。还有一些问题有待解决。

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.