ARTICLE IN PRESS Applied Ocean Research ( ) – Contents lists available at ScienceDirect Applied Ocean Research journal homepage: www.elsevier.com/locate/apor Application of a vortex tracking method to the piston-like behaviour in a semi-entrained vertical gap T. Kristiansen ∗ , O.M. Faltinsen Centre for Ships and Offshore Structures (CeSOS), Norwegian University of Science and Technology (NTNU), N-7491, Trondheim, Norway Department of Marine Technology, Norwegian University of Science and Technology (NTNU), N-7491, Trondheim, Norway article info Article history: Received 4 December 2007 Accepted 18 February 2008 Available online xxxx Keywords: Vortex tracking method Boundary layer effect Numerical wavetank Moonpool 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. © 2008 Elsevier Ltd. All rights reserved. 1. Introduction The water motion in a semi-entrained volume of fluid with a free surface may experience resonant behaviour with respect to the different possible free surface modes when undergoing external forcing among which the lowest mode, often referred to as the piston mode and corresponding to the vertical motion of the mean free surface has drawn the attention of several authors, including [1–3]. The main focus in these works was, in the framework of linear potential theory, to identify the resonance frequencies of the piston mode. The piston mode amplitude was also investigated. Near resonance the piston mode amplitude may become large relative to the amplitude of the exciting mechanism, with the consequence of among other things large forces on the structures actually defining the semi-entrained volume. However, linear theory is known to over-predict the fluid response with respect to experimental results in such semi-entrained systems. In practice this has been remedied by introducing artificial damping ∗ Corresponding author. Tel.: +47 73595629; fax: +47 73595528. E-mail address: trygve.kristiansen@ntnu.no (T. Kristiansen). coefficients in the free surface conditions, with the values tuned from e.g. model test results. However, the introduction of such artificial damping coefficients is purely empirical and not based on physical reasoning. It is a pragmatic approach taken due to the yet poorly understood mechanism for the discrepancy. Therefore, an investigation of the physical mechanisms contributing to the discrepancy is of interest, and we feel that the present work provides new insight into the matter. In principle, the attention of the present discussion is on any arrangement consisting of a well-defined vertical gap, or inner domain of some sort connected with an outer domain allowing radiated waves to escape. Practical examples of such semi-entrained systems are moonpools (vertical openings through the decks of ships), ship-by-ship operations or a ship by a terminal. The results in the present work are directly compared to the results in [3] where they investigated piston-like sloshing in a moonpool, or similarly, in between the hulls of a catamaran. In terms of a linear mass–spring system the response is sensitive to the magnitude of the damping when this is small. Linearly, only wave radiation contributes to damping while in reality, two additional mechanisms may affect the piston mode motion. The first being the effects of viscosity. Assuming high Reynolds numbers this includes in- and out-flow of boundary 0141-1187/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.apor.2008.02.003 Please cite this article in press as: Kristiansen T, Faltinsen OM. Application of a vortex tracking method to the piston-like behaviour in a semi-entrained vertical gap. Applied Ocean Research (2008), doi:10.1016/j.apor.2008.02.003