The experiment of flow with free surface around a planing rectangular plate with small attack angle in the circulating water channel is described. And the computational technique to solve the Navier Stokes equations numerically is introduced, explaining the detailed scheme of numerical computation, the body-fitted coordinate systems and the concrete finite differentiations.
The computational method was applied to the wave problems generated by a planing plate and the calculated wave profiles were compared with the experimental ones in details. As the results, the computational technique is proved to be almost satisfactory, in spite of remaining several problems to be solved in the future.
1. INTRODUCTION
The hydrodynamic problems of a planing plate are important for the high-speed craft dynamics, and among them the problem of waves generated by a planing plate has been an interested target. In the past, the resistance of the planing plate was focused on, and many researchers engaged to research on the wave making resistance and frictional resistance problems. In the first, Wagner treated the two dimensional wave phenomena generated by a planing plate of the infinite span. and successively, Green, Sedov and others developed the similar problems1)-3)
However, most of these works were in analytical methods and could solve only the case of simplified problems. In numerical computations of flow with free surface around a planing flat plate at higher Froude number, scarcely work has been made.
The purposes of this research are to introduce a numerical computational technique of Navier-Stokes equations and applying it to the wave problems generated by a planing plate. This technique is a kind of the finite difference method similar to MAC schemne, and the characteristics of the present method are to adopt a body-fitted coordinate system. non-staggered mesh system and third-order upstream difference for the convcetion terms in the Navier-Stokes equations.
The computed surface waves are compared with the experimental ones generated by a planing flat plate of the finite span. The experiments were carried out in the circulating water channel. The waves and the pressure distribution on a planing plate were measured and were compared with calculated ones.
2. WAVE MEASUREMENT IN A CIRCU-LATING WATER CHANNEL
The experiments of waves generated by a planing plate were performed in the circulating water channel of Hiroshima College of Mercantile Marine. Fig. 1 shows the outlines of the circulating water channel and generated waves. The length of experimental section of the water channel is 3.0m, its width is 1.2m, depth is 1.24m and the
Fig. 1 Waves generated by a planing plate in a circulating water channel
