| Summary: | Ocean waves are an increasingly attractive target for renewable energy technologies, spurring the development of tools to optimize the capture of this available energy. While there has been an abundance of wave energy converter (WEC) concepts developed over the last 50 years, few have been commercially realized due in part to the challenges in assessing an optimal design. Design efforts have sought to maximize energy generated from WECs by optimizing nonlinearities in the power take off (PTO) mechanism, controls, and, more recently, geometry, while often assuming linear hydrodynamics and small body motions. Yet, in the most energetic sea states, large WEC motions and hydrodynamic nonlinearities may become appreciable, potentially resulting in a mismatch between the real-world performance and the performance predicted by linear theory. Existing nonlinear hydrodynamic models face a combination of high computational cost, numerical sensitivity, and complex user interfacing, rendering them impractical or restricted to specific geometries and conditions.
This thesis introduces a novel and robust approach to simulating the nonlinear hydrodynamics and large response motions of floating WECs and general bodies in stochastic waves. The dominant incident wave Froude-Krylov and hydrostatic nonlinearities are expressed as volume integrals using Fluid Impulse Theory. The proposed framework debuts Quasi-Monte Carlo (QMC) spatial integration in nonlinear wave-body interactions, in conjunction with a new extension of Modified Chebyshev Picard Iteration compatible with the fluid force impulses. A mesh-free geometric representation using signed distance functions circumvents the numerically sensitive mesh-mesh surface intersection at each time step, and a continuously differentiable boundary blur accelerates the QMC convergence. These algorithms have been implemented in a parallel-time Julia code, which is studied on several canonical problems to understand the fundamental behavior of this framework.
The performance of the blurred-boundary QMC integration algorithm is assessed on a fixed cylinder, demonstrating rapid convergence of the nonlinear incident wave Froude-Krylov impulses and convergence of the hydrostatic forces. The robust time-integration of the equation of motion is demonstrated with a heaving cylinder and applied to a surging tension leg platform that forms the basis of a new WEC concept under development. These studies indicate very promising perfor- mance without observing adverse numerical sensitivity that may limit the simulation time span, or the need for delicate mesh preparation. This framework has the ability to support optimal design studies, taking into account the interaction between hydrodynamic, geometric, dynamic, PTO and control nonlinearities. The potential of this method extends to more general ship seakeeping studies, where (hydro)dynamic nonlinearities can become important in severe stochastic waves.
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