Research Article Mathematical Framework for Hydromechanical Time-Domain Simulation of Wave Energy Converters J. Seixas de Medeiros 1 and S. Brizzolara 2 1 Massachusetts Institute of Technology, 77 Massachusetts Avenue, Room 5-423, Cambridge, MA 02139, USA 2 Virginia Tech, Randolph Hall, RM 332-4, 460 Old Turner St., Blacksburg, VA 24061, USA Correspondence should be addressed to J. Seixas de Medeiros; joaosm@mit.edu Received 1 September 2017; Accepted 7 December 2017; Published 17 January 2018 Academic Editor: Renata Archetti Copyright © 2018 J. Seixas de Medeiros and S. Brizzolara. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Efcient design of wave energy converters based on foating body motion heavily depends on the capacity of the designer to accurately predict the device’s dynamics, which ultimately leads to the power extraction. We present a (quasi-nonlinear) time-domain hydromechanical dynamic model to simulate a particular type of pitch-resonant WEC which uses gyroscopes for power extraction. Te dynamic model consists of a time-domain three-dimensional Rankine panel method coupled, during time integration, with a MATLAB algorithm that solves for the equations of the gyroscope and Power Take-Of (PTO). Te former acts as a force block, calculating the forces due to the waves on the hull, which is then sent to the latter through TCP/IP, which couples the external dynamics and performs the time integration using a 4th-order Runge-Kutta method. Te panel method, accounting for the gyroscope and PTO dynamics, is then used for the calculation of the optimal fywheel spin, PTO damping, and average power extracted, completing the basic design cycle of the WEC. Te proposed numerical method framework is capable of considering virtually any type of nonlinear force (e.g., nonlinear wave loads) and it is applied and verifed in the paper against the traditional frequency domain linear model. It proved to be a versatile tool to verify performance in resonant conditions. 1. Introduction We will frst introduce the standard mathematical approach followed to evaluate performance of wave energy converters (WECs), whose design requires early quantifcation of the new device’s power extraction capabilities. Concepts which rely on a foating body’s motion in waves for power extraction have taken advantage of methods created to simulate motion of ships and ofshore structures. Te very frst objective is to tune the converter’s natural frequency (of its translation and rotation considered motions) with the predominant wave period from the operating site spectrum. Traditionally, the waves and equations of motion are linearized (i.e., small wave amplitude and body motion compared to the device’s nominal size), potential fow is assumed with Laplace as the governing equation (i.e., ∇ 2 =0), and the resulting linear Boundary Value Problem (BVP) to be solved for is summarized in Table 1. Te most common approach to study the body’s motion is to assume harmonic inputs (i.e., force   cos(  →   → −+  ) due to an incident regular wave  cos(  →   →  − )), for which the linear equation of motion, with frequency , becomes 6 ∑ =1   [− 2 (  +  ())+  ()+  ]=  . (1) Te linearization of the motion allows a decomposition of the total fuid potential as a summation of the classical radiation and difraction wave potentials [1]. Te former models the waves generated by the moving body (with the same frequency as the incident wave) in calm water. It can be represented by the summation of each degree of freedom (DoF) displacement, subject to its own body BC [2]. =  +  =  +  +  , where    =0. (2) Hindawi Mathematical Problems in Engineering Volume 2018, Article ID 1710253, 15 pages https://doi.org/10.1155/2018/1710253