Effect of Gravity on the Vertical Force of an Oscillating Wedge at Free Surface Master of Science Thesis For the degree of Master of Science in Offshore and Dredging Engineering at Delft University of Technology

As for a ship oscillating at free surface with frequency that ranges from those that are common for ship motion in waves to very high frequency associating with the impact problem, the vertical force acting on the ship for the lower limit of frequency range is dominated by gravity effect, which is usually ignored in the impact theory. As a consequence there must be a transition range in between those gravity-dominant and gravity-negligible conditions. Indeed these two limiting conditions have been studied deeply by many researchers for decades, but the transition range has not gain much attention. This thesis concerns the determination of the limit for each of these extreme conditions and the quantification of the gravity effect in this transition frequency range. The hydrodynamic load caused by ship motion in waves normally is estimated by linear potential BEM in which the free surface boundary condition is linearized on the undisturbed water level, while the assessment of impact induced load mainly involves momentum method and nonlinear potential BEM. To be able to deal with nonlinearity that the linear potential theory is lack of and gravity effect that the impact theory ignores, it is necessary to apply a CFD method to study the fluid domain. In this thesis, the CFD method is based on the Navier-Stokes equations for an incompressible, viscous fluid with a numerical discretization of the finite volume method. To simplify the simulation, wedge-shaped bodies with deadrise angle of 15o, 30o and 45o are used to represent the cross section of a ship. The thesis starts with defining the limit of gravity-dominant condition, in which both linear potential BEM and CFD method are applied. By comparing the hydrodynamic coefficients of added mass and damping, the application limit of linear potential theory is found as well and an estimation method is developed for determining the limits. In the slamming-frequency oscillations, in addition to the CFD simulations, momentum method and 2D-BEM proposed by Zhao, Faltinsen and Aarsnes are also used to calculate the impact loads. The vertical forces are compared with each other to verify the accuracy. By concerning the relative gravity force to the total, the limits of gravity-negligible condition are obtained. Finally, after determining the limits of those two extreme conditions, the quantification of the gravity effect is performed by applying the simulations with and without gravity acceleration in CFD program.