Numerical Modeling of Compliant-Moored System Dynamics with Applications to Marine Energy Converters

Abstract

The development of a numerical model simulating the dynamic response of compliant-moored submerged systems to non-uniform fluid flow is presented. The model is meant to serve as a computational tool with applications to compliant-moored marine energy converters by time-domain representation of the mooring dynamics. The scope of the initial code is restricted to full-submerged moored tidal turbines, though the model can be readily expanded to analyze wave energy converters as well. The system is modeled in a Lagrangian frame treating tidal turbines and structural elements as rigid bodies. Mooring lines are modeled as a series of discrete elastic segments, with parameters and force contributions lumped to point-mass nodes joining each segment. Full-range of motion is achieved using the α-β-γ Euler Angle method. The governing equations of motion of the system are derived computationally through implementation of Lagrange's Equation of Motion. The techniques employed to develop the symbolic expressions for the total kinetic, potential, and damping energies of the system and the forces acting on each element of the system are discussed. The system of differential equations obtained from evaluation of Lagrange's Equation with the developed symbolic expressions is solved numerically using a built-in MATLAB ordinary differential equation solver called ODE15i.m with the user defined initial condition of the system. Several validation tests are presented and their results discussed. Finally, an explanation of future plans for development of the model and application to existing tidal energy systems are presented.