Application of a vortex tracking method to the piston-like behaviour in a semi-entrained vertical gap

Abstract

Near resonance the piston mode amplitude in semi-entrained volumes of fluid such as in moonpools or in between a ship and a terminal may become large relative to the level of excitation. Linear theory is known to over-predict the fluid response in these types of systems significantly, suffering from the lack of damping whose only manifestation is radiated waves. In reality, however, viscous effects may act as damping and nonlinear effects associated with the free surface conditions may cause transfer of energy between the different modes. In the present work, which is within the framework of potential theory, a fully nonlinear numerical wavetank based on Green’s 2nd identity coupled with an inviscid vortex tracking method is applied to the moonpool problem. The paper presents a methodology for perpetual simplification of the free shear layer as the system undergoes near sinusoidal motion in order to reach steady state. This is practically impossible without such simplifications due to the otherwise exceedingly complex wake structures evolving only after the first one or two periods. Also the in- and out-flow of the boundary layers are modelled. The results are compared to experiments. In the investigated cases models of rectangular shape with sharp corners provide well-defined separation points, and such sharp corners are in practice introduced e.g. by bilge keels. It is found that: (1) The damping effect associated with the nonlinear free surface conditions are of minor importance, (2) the effect of the in- and out-flow of the boundary layer is negligible to all practical purposes, whereas (3) the flow separation explains the major part of the discrepancy between the measured response and that estimated by linear theory.