Yingyi Liu

This paper presents WSMAQ (WEC-Sim-MoorDyn-AeroelasticQ), a coupled aero-hydro-elastic-mooring simulation framework for floating offshore multi-rotor wind turbines. The framework integrates WEC-Sim for platform hydrodynamics; MoorDyn-C for mooring-line dynamics; and in-house aeroelastic code, AeroelasticQ, for rotor-level aerodynamic and blade structural calculations. These modules are coupled within MATLAB/Simulink/Simscape 2023a. The novelty of WSMAQ lies in three coupling-oriented methodological extensions. First, for deep-draft spar platforms, the WEC-Sim body is configured using the physical mass and inertia at the true center of gravity, the full unadjusted added-mass matrix is retained in the radiation-load calculation, and a three-block integrator filter is used to break the added-mass–acceleration algebraic loop. Second, the WEC-Sim mooring class is extended to pass the non-zero initial platform orientation to MoorDyn-C. Third, AeroelasticQ is integrated with the multibody wind turbine model through a rotor-count-parameterized Level-2 C++ MEX S-function. The framework was benchmarked against OpenFAST through aeroelastic, platform-mooring, and full-wind-turbine tests on the OC3 spar with the 5 MW reference turbine developed by the National Renewable Energy Laboratory. Across the primary response channels, the mean relative error remained below 2% in most cases. Multi-rotor capacity was demonstrated using three NREL WindPACT 1.5 MW turbines mounted on the OC3 spar. In this case study, an asymmetric rotor-parked condition generated a mean yaw offset of approximately 4°, which did not appear in the symmetric-load cases.

A hybrid system combining wave energy converters (WECs) and a floating breakwater presents significant potential for developing commercial-scale wave power operations. The assessment of the hydrodynamic characteristics of a WEC array–floating breakwater system under irregular waves remains in the early stages and requires further investigation. Based on the linear potential theory, a time-domain numerical model is established to evaluate the performance of a hybrid WEC array–floating breakwater system in a target sea area. The interaction between the WECs and the floating breakwater is analyzed. Results show that for the hybrid system with a triangular-baffle-type WEC array under irregular waves, the annual average wave power is 1.16 MW and the annual energy production is 10.16 × 10³ MW·h, representing a 241.2% improvement compared with that of the isolated WEC array. The standard deviations of the mooring forces for the hybrid system with the triangular-baffle-type WEC array are reduced by 13.8% in the surge direction and 26.9% in the pitch direction, while increasing by 90.0% in the heave direction. Similar conclusions are obtained for the motion of the floating breakwater. The findings and data reported in this study provide guidance for the engineering application of a hybrid WEC array–floating breakwater system.

Periodic offshore structures are extensively utilized in coastal and offshore engineering; however, their hydrodynamic analysis poses significant challenges due to the substantial computational resources and storage required for large-scale problems. To address these challenges, an accelerated higher-order boundary element method (HOBEM) is proposed. This approach leverages the translation invariance of the Green's function to exploit the block Toeplitz structure inherent in the coefficient matrix of the discretized boundary integral equation. The dense matrix is systematically decomposed and embedded in a block circulant matrix, enabling the use of a fast Fourier transform-based iterative computational strategy. This forms a high-performance framework for matrix operations, integrating HOBEM with a fast Toeplitz-type matrix solver (FTMS), herein referred to as HOBEM-FTMS. Extensive numerical investigations demonstrate the accuracy, robustness, and computational efficiency of the proposed method. Case studies involving floating buoy arrays, hinged floating bridges, and offshore photovoltaic arrays validate their applicability to a wide range of periodic structures and elucidate the coupled effects of structural parameters, array configurations, mechanical constraints, and wave conditions. The results further indicate that resonance-prone behavior in periodic arrays can be strongly influenced—and in some cases effectively suppressed—not only by wave conditions and array geometry, but also by structural connectivity and mechanical constraints.

The wave-induced hydrodynamics of coupled nonlinear piston-mode fluid resonances within two narrow gaps between three barges are numerically investigated using a two-dimensional viscous wave flume. This study aims to explore the time-dependent nonlinear interactions between fluid oscillations in the two gaps. The coupled synchronous dynamic behaviors of fluid oscillations during the transient evolution stage are first examined in terms of amplitude and frequency modulation. It is shown that phase dynamics, including phase slipping, trapping, and locking, play significant roles in establishing the coupled synchronous dynamic evolutions of fluid oscillations in the two gaps. The quasi-steady state of the amplitude- and phase-frequency responses of fluid oscillations within the gaps, along with the reflection and transmission waves in front of and behind the three-barge system, are further analyzed. This analysis clarifies the significance of viscous damping energy dissipation and radiation damping energy transfer involved in gap resonance problems. This clarification also explains the performance of fully nonlinear potential flow solvers in predicting fluid resonances in the two narrow gaps. Finally, the nonlinear dynamic features of fluid oscillations are examined. The effects of incident wave nonlinearity, i.e., wave steepness, on resonant frequencies, response amplitudes, energy dissipation, and reflection and transmission coefficients are investigated. Harmonic analysis via Fourier transformation reveals the contributions of first-, second-, and third-order harmonics to the overall response amplitudes. The physical insights gained from this study provide a deeper understanding of the coupled nonlinear dynamics of piston-mode fluid resonances in multiple narrow gaps.

The computation of the second-order mean wave drift loads on a body with thin perforated shells is fundamental and relevant to a wide range of applications in marine engineering, marine aquaculture, offshore renewable energy, etc. In this work, formulations involving a control surface at a distance from the body are proposed to compute drift loads on structures composed of an impermeable hull and a perforated surface accurately and efficiently. Applications of mathematical identities and conservation of fluid momentum are proved to yield identical formulations. Due to the presence of perforated shells, an integral caused by the dissipation through perforated surfaces is included in the formulation. The present formulation cannot only give all six components of the mean wave drift force and moment, but also determine the drift loads on each individual body of a multibody system. The developed formulations are applied to a series of structures, including single-body and multibody systems. It is found that the perforated surface integral plays a secondary role in the computation of drift loads. Besides, perforating body surfaces can mitigate the near-trapped wave motion in a multibody system. Compared to a fixed system, the mean wave drift loads can be amplified around the resonance frequencies of body motions. The dissipation through the perforated shell can enhance the damping effect and suppress the excessive motion response, resulting in a reduction in the amplified drift loads.

Natural sea waves are typically multi-directional. However, the existing studies on the interaction of waves and structures mostly concentrate on uni-directional waves. In this study, using a higher-order boundary element method based on the nonlinear potential flow theory and the perturbation expansion technique, a numerical model is developed to investigate the hydrodynamic performance of a semi-submersible wind turbine foundation in uni- and multi-directional waves. Comprehensive validations with the wave-tank experiment are conducted. It is found that the significant platform response increases with the peak wave period in uni-directional irregular waves, while the high-frequency “energy” ratio changes little. The significant wave height hardly influences motion responses from either the time- or the frequency-domain perspective. In multi-directional irregular waves, the translational motions exhibit monotonicity with wave directionality. The energy concentration around the primary direction leads to a dominant wave-frequency motion and an increase in the high-frequency “energy” ratio. Although the individual modal motion responses are variable functions of wave nonlinearity, their averaged translational and rotational motions are nearly constant, indicating an energy transition or a trade-off relationship among the modal motions. In addition, unlike the uni-directional wave case, the low- and high-frequency “energy” ratios increase quadratically and decrease linearly with the significant wave height in multi-directional waves, respectively. All these findings demonstrate that wave directionality can change the wave–structure interaction properties and therefore needs to be adequately considered in engineering applications.