Nonlinear Transient Motion Of Deep Ocean Mining Pipe

Field: Engineering (Physical Sciences)

ABSTRACT For accurate and economic time-domain analysis of deep-ocean mining pipes, a realistic representation of hydrodynamic forces along the pipe and an efficient numerical method are required. A transient analysis procedure is formulated and implemented for the numerical determination of nonlinear transient motion of pipes using, as an initial condition, the nonlinear static configuration. The pipe is modeled by three-dimensional beam finite elements which account for coupled axial, bending and torsional deformations. We used (1) vertical variation of seawater properties and hydrodynamic force in the stratified ocean, (2) relative pipe velocity and response for each state in the force computation, and (3) an implicit-time-integration method. Several cases are presented for accelerating, turning, and oscillatory motions of the ship and an 18,000-ft pipe, bottom end free. The subsurface environment and force coefficient selection greatly affects the results. The method can be directly applied to the analysis of deep sea risers and OTEC pipes. INTRODUCTION It is necessary to simulate the motion of the pipe bottom in the time domain to aid the design of a mining system and position-control operation system. In addition, for the deep-ocean mining application, we need such simulations for the (control) operation simulation of the ship-pipe-miner system maneuvering. For design applications, the linear frequency-domain solution has been previously used, since it is cheaper though less accurate. However, the (control) operation simulation requires nonlinear, transient pipe response solutions (e.g., accelerating/ starting, decelerating/ stopping, and wave-induced, ship-motion-induced, or self-induced oscillation). To carry out time integration for the transient solution, a technique which allows for the use of large time steps should be devised to reduce the time integration cost. Selection of an economical time step size (variable or fixed) has conflicting requirements with numerical stability and computational accuracy. Furthermore, deep-ocean or very long pipe configuration can become geometrically nonlinear. The substantial torsional deformation appears to be unique to such an l8,000-ft long pipe system. Combined velocity and size requirements of the pipe for the mining system operation happen to fall into the transition Reynolds (Re) number range where the drag coefficient vs. Re curves of the pipe are very steep. Also, the vertical variation of the subsea current velocity and fluid properties (in particular, the viscosity) and local pipe response motion at the element level vary Re and hydrodynamic force (dominantly drag) coefficients vertically along the pipe. Thus, both the estimate accuracy of the hydrodynamic drag or damping, and the subsequent pipe responses depend on the modeling of the environment, ship motion, and hydrodynamic forces [1]. Additionally, uncertainties in the drag coefficient data can greatly change the accuracy of the predicted pipe responses in both static pipe-bottom excursion and dynamic motion which are needed to determine the nodule mining efficiency and the pipe system operation.