Seakeeping Performance Analysis by Nonlinear 2D+t Slender-Ship Theory

Abstract

The operability of marine craft and coastguard vessels in heavy seas is primarily restricted by the occurrence of large amplitude motions, slamming, and deck-wetness. These effects result from ship–wave interactions which are characterized by local highly nonlinear flows beyond the scope of linear seakeeping theory. However, linear methods are preferably employed and confided in during the early ship design in order to generate optimized hull shapes regarding partly conflictive objectives like low resistance, efficient propulsion, and satisfactory seakeeping performance. Thus, model tests or detailed numerical investigations have to be conducted in succession for the verification of the preliminary design. This paper presents a pragmatic computational approach to the assessment of seakeeping performance for fast and slender ships. The consistent investigation of nonlinear ship motions must consider both, geometric and hydrodynamic nonlinearities. A promising approach, with regard to efficiency, is provided by the so-called 2D + t theory which has been successfully applied to the prediction of high-speed craft wave resistance and deck-wetness problems. For a comprehensive review of the 2D + t theory we refer to [4]. Following the lines of slender-body theory, the three-dimensional flow problem is reduced to a number of two-dimensional problems for the free surface flow perpendicular to the ship forward motion, see Fig. 1. Classically, the nonlinear two-dimensional free surface flow is computed assuming potential flow theory by the Mixed Eulerian–Lagrangian method [2, 6]. Recently, however, volume-of-fluid schemes for viscous flow computations have been employed in combination with the 2D + t approximation [1]. Until present, the 2D+ t theory has been applied predominantly with the focus on wave built-up and jet generation in the ship’s bow region while the ship follows prescribed motions as determined by a linear sea-keeping theory. Here, we will compute the motions of a ship in waves directly from the pressure field obtained by the nonlinear 2D + t theory. With the investigation of the nonlinear hydrodynamic effects on the coupled heave–pitch–roll motions, we