Modelling and simulation of low-tension oceanic cable/body deployment

This study presents a general set of three-dimensional dynamic field equations, boundary conditions and a computational algorithm for time simulation of low-tension oceanic cable/body deployment.^ The dynamic equations of motion for a cable segment are derived in the principal torsional-flexural axes of a cable cross-section and are based on the classical Euler-Kirchhoff theory of an elastica. Unlike the traditional model for a slender, perfectly flexible cable, the present formulation includes shear flexural, torsional and inertia effects. The addition of the flexural or torsional stiffness, albeit small, provides the necessary mechanism by which energy is transferred across a low-tension region, hence removing the potential singularity when the cable tension vanishes and enhancing stability of the solution. The Euler angles, representing the rotation of the cable segment, are carefully selected to minimize the possibility of coordinates transformation breakdown. The general field equations written in a generic form by index notation also apply to two-dimensional problems and can be reduced to the equations of a perfectly flexible cable.^ The kinematic and dynamic boundary conditions are specified. To treat terminal and intermediate boundaries along the cable scope, boundary conditions are developed from the dynamic equilibrium equations for a general ellipsoid using translational and rotational degrees of freedom. To improve the numerical stability when handling larger payout speeds, a special treatment for payout conditions is developed by decoupling the payout velocity from the total velocity. The touchdown boundary conditions are also defined to meet the nonpenetration and nonadhesion conditions imposed at the seafloor.^ The dynamic field equations are integrated in time by a stable implicit integration scheme. A stepwise integration process in space and an iterative Newton-Raphson method are adopted to solve the nonlinear boundary-value problem in cable spatial coordinates. A hybrid model and solution algorithm in which bending stiffness is admitted only in the low-tension region is investigated in order to develop a more efficient solution process for cases in which bending is predominantly negligible.^ The developed computer code is used to study various applications including a towed cable with a free end, a towed cable/body undergoing complex vessel maneuvers, a cable/multi-body payout and cable/multi-body touchdown problem. The results for the complete elastica model and for the hybrid model are compared with those obtained with a perfectly flexible cable model.