Numerical Research Of Wave-making Resistance For Trimarans

A trimaran with a slender or super slender main hull and two small outriggers is a kind of promising new ship forms with many special advantages. For this ship, the wave-making resistance is of particular importance, on which domestic and foreign scholars have conducted a lot of researches.The lateral "lift" caused by the asymmetry of the flow around outriggers of a trimaran generally has some non-zero component in the moving direction of a trimaran and then affects the ship resistance. Numerical calculations of the wave-making problem for a trimaran based on potential theory with or without consideration of this effect are both presented in the references up to now. The main purpose of this paper is to discuss the effects of asymmetry of the flow around outriggers of a trimaran on the results of numerical calculations of the wave-making problem for the trimaran.The numerical calculation of wave-making resistance by a raised panel method based on NURBS (Non-Uniform Rational B-Splines) for trimarans is discussed. This is a high-precision and generalized higher-order panel method, in which the body surface, free surface and other physical quantities to be solved are expressed as a whole nth-order continuous surface, or several surfaces if needed. Compared to conventional panel methods, it is of better numerical characters. Raised panels above the free surface combined with collocation-point shifting up-stream are used to satisfy the radiation condition numerically.A non-uniform rational B-Splines (NURBS) method to design curves and surfaces is summarized and fits of three-dimensional hull surface adopt the skinning method is carried out. An expansion to the calculations in restricted waters is considered in numerical calculating programs. The programs can generate NURBS surfaces from the input of discrete geometry data of the water bottom or bank, and calculate corresponding problems.Because a transom-stern condition such as the free surface flow detaches smoothly from the bottom of the transom is similar to the so-called Kutta condition in a sense, special numerical treatments are then not needed in calculations for transom-stern hulls. A distribution of vortices on the center plane of the outriggers without transom-stern is used to simulate the effect of lift caused by the asymmetry of the flow around outriggers of a trimaran. By satisfying the kinematic boundary condition on the wetted ship surface, the linear free surface boundary conditions on the free surface, the radiation condition and the equal-pressure Kutta condition at the trailing edge, the unknown source densities and vortex densities can be calculated. The hydrodynamic force and then the wave-making resistance with the consideration of the asymmetric flow are determined.Wigley hull is selected as the computational example in deep water condition. Numerical calculation is carried out to obtain wave-making resistance and wave pattern in condition of ignoring the asymmetry of flow field and considering the asymmetry of flow field respectively. Compared with the corresponding experiment data and calculated data in other references, the results are reasonable.