Numerical Modeling of a Spar Platform Tethered by a Mooring Cable

Virtual simulation is an economical and efficient method in mechanical system design. Numerical modeling of a spar platform, tethered by a mooring cable with a spherical joint is developed for the dynamic simulation of the floating structure in ocean. The geometry modeling of the spar is created using finite element methods. The submerged part of the spar bears the buoyancy, hydrodynamic drag force, and effect of the added mass and Froude-Krylov force. Strip theory is used to sum up the forces acting on the elements. The geometry modeling of the cable is established based on the lumped-mass-and-spring modeling through which the cable is divided into 10 elements. A new element-fixed local frame is used, which is created by the element orientation vector and relative velocity of the fluid, to express the loads acting on the cable. The bottom of the cable is fixed on the seabed by spring forces, while the top of the cable is connected to the bottom of the spar platform by a modified spherical joint. This system suffers the propagating wave and current in the X-direction and the linear wave theory is applied for setting of the propagating wave. Based on the numerical modeling, the displacement-load relationships are analyzed, and the simulation results of the numerical modeling are compared with those by the commercial simulation code, Proteus DS. The comparison indicates that the numerical modeling of the spar platform tethered by a mooring cable is well developed, which provides an instruction for the optimization of a floating structure tethered by a mooring cable system.

Numerical Modeling of a Spherical Buoy Moored by a Cable in Three Dimensions

Floating facilities have been studied based on the static analysis of mooring cables over the past decades. To analyze the floating system of a spherical buoy moored by a cable with a higher accuracy than before, the dynamics of the cables are considered in the construction of the numerical modeling. The cable modeling is established based on a new element frame through which the hydrodynamic loads are expressed efficiently. The accuracy of the cable modeling is verified with an experiment that is conducted by a catenary chain moving in a water tank. In addition, the modeling of a spherical buoy is established with respect to a spherical coordinate in three dimensions, which can suffers the gravity, the variable buoyancy and Froude-Krylov loads. Finally, the numerical modeling for the system of a spherical buoy moored by a cable is established, and a virtual simulation is proceeded with the X- and Y-directional linear waves and the X-directional current. The comparison with the commercial simulation code Proteus DS indicates that the system is accurately analyzed by the numerical modeling. The tensions within the cable, the motions of the system, and the relationship between the motions and waves are illustrated according to the defined sea state. The dynamics of the cables should be considered in analyzing the floating system of a spherical buoy moored by a cable.