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

点击翻译按钮获取中文摘要

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.