The hydrodynamics of ship sections entering and exiting a fluid

Abstract

We study the hydrodynamics of wedge,knuckle and box cross-sectional profiles undergoing transient extreme motions, in particular forced entry and exit at constant velocity or acceleration. Extensive data for the forces, pressures and free-surface profiles is generated by an extension of a fully-nonlinear boundary-integral method. The code is thoroughly checked by altering the time step and particle spacing on the bodies and Lagrangian free-surface markers, and, for the wedge,checking self-similarity for the infinite Froude number (gravity free) constant velocity entry. Difficulties with inviscid flow around sharp corners are discussed. Results for exit are of particular interest since no zero-gravity approximation is valid and this precludes application of existing slamming theories in reverse. Whilst entry generally gives larger free-surface motions (spray jets), pressures and hence forces, calculation of exit is needed for the velocity of subsequent slamming and so is of practical interest too. These results are compared with an approximate analytical model, based on Schwarz-Christoffel transformations to calculate the infinite-frequency added mass of the cross-section below the mean water line. For constant acceleration of both entry and exit, the analytical theory is good during the early stages of motion. Later, the assumption of an undisturbed mean water level is clearly violated; the exact calculations show a large amount of draw-down (up-rise), the free-surface making contact with the body well below (above) the mean water level. We therefore examine the effect of reducing (increasing) the submerged body volume to take account of this, which prolongs the agreement between the results considerably and therefore might be used to improve practical calculation of extreme ship motions using existing strip theory codes. Full sets of numerical data input/output are provided in the appendices, together with some mathematical details. We also speculate on the possible application of John's equation to wedge entry.