Gap problems refer to a class of hydrodynamic problems that include, for instance, the analysis of flow in moonpools, between ships in side-by-side configuration, and between a ship and a terminal. For all those problems, the coupled motions of the structure and of the entrapped fluid column, under various wave conditions, are decisive for operability assessments.
Classical potential theory seriously over-estimates ship and fluid motion under near-resonant conditions. This is due the absence of physical modelling of the flow separation and vortex shedding near sharp corners, which have a damping effect on the piston-like fluid motions in the gap. Examples of such sharp corners are bilge keels, damping plates, moonpool edges, or simply platform pontoons.
In the course of a three-year research project, MARINTEK performed numerical and experimental studies of this phenomenon. Three distinct numerical approaches were involved. The first was a fully nonlinear time-domain BEM code that included an inviscid vortex-tracking method. The vortex-tracking method follows the separated free-shear layer in time. This method provided accurate results but lacked robustness. Moreover, in practice the approach is limited to two-dimensional flow studies, although the formulation is valid also in three dimensions. The second method was a Finite Volume Method combined with a Volume of Fluid approach to capturing the interface. The main difficulty related to this method was that it was computationally resource-intensive. A third approach, which is currently under development, is a hybrid Finite Volume Method. Hybrid refers to the fact that it combines “potential” and “Navier-Stokes” domains, which make it highly suitable for the study of resonance problems in which both waves and flow separation matter.
A snapshot from a moonpool simulation using the vortex-tracking method is shown in Figure 1(a). The box-shaped hull was forced to heave in sinusoidal motion at the natural frequency of its moonpool, causing a large piston-like water motion. The figure illustrates that the shed free-shear layer (vortex) from the sharp inlet edge caused a back-flow at the moonpool inlet, thus providing damping. A snapshot from a simulation using a two-dimensional hybrid code in a similar moonpool case is shown in Figure 1(b), where a similar vortex structure can be observed.
The results of a validation study of the hybrid method are shown in Figure 2. The agreement is good and the computational time required was low. One simulation that ran 30 wave periods with 80 time-steps per period (2400 time-steps) took only 73sec on a 2.4GHz PC.
References
[1] Kristiansen, T., Two-dimensional numerical and experimental studies of piston-mode resonance, PhD thesis, Norwegian University of Science and Technology (2009)
[2] Kristiansen T and Faltinsen, O. M., Gap resonance analyzed by a domain decomposition method, 26th Int. Workshop on Water Waves and Floating Bodies (2011)
To see the figures in this article, please open the pdf version of the article in MARINTEK Review No. 2-12
