A Reynolds-Averaged Navier-Stokes (RANS) numerical method has been coupled with a six-degree-of-freedom motion program for time-domain simulation of ship and fender coupling during berthing operations. The method solves the mean flow and turbulence quantities on embedded, overlapped, or matched multiblock grids. The unsteady RANS equations were formulated in an earth-fixed reference frame and transformed into general curvilinear, moving coordinate systems. A chimera domain decomposition technique was employed to accommodate the relative motions between different computational blocks. Calculations were performed first for a full-scale motor vessel in berthing operations. Comparisons have been made between the computations and measurements to demonstrate the feasibility of the chimera RANS approach for time-domain simulation of the hydrodynamic coupling between the ship and berthing structures. The method was then employed for a parametric study of full-scale berthing ships under different approach speeds, water-depth-to-draft ratios, quay wall clearance distances, and fender stiffnesses.


Damage due to berthing operations can result in substantial financial and operational penalties to ships and wharves. Even in a well executed berthing, a large ship possesses enormous kinetic energy that could seriously damage the berthing structure as well as the ship itself. Fender systems are provided at a berth to absorb and dissipate the kinetic energy of the berthing ship and to mitigate impact forces. The amount of energy absorbed and the maximum impact force imparted are the primary criteria applied in accepted fender design practices. However, because berthing is a highly complex process that involves structural and fluid coupling between a vessel, a fender system, and the surrounding water, a reliable and accredited assessment tool for computing berthing energy has to date not been developed. Currently, most accepted fender design methods (e.g., Fontijn, 1988) account for the influence of the ambient water by using a simple constant coefficient.

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