Response Amplitude Operators Research Articles

An Experimental and Numerical Study of Motion Responses of Multi-Body Arrays with Hinge Connections

Hinged multi-body systems are gaining popularity in the field of ocean engineering. Their performance is commonly evaluated using numerical simulations, but comparisons with experimental data are required to ensure the accuracy of the computational tools. However, there is a dearth of experimental studies on the motion performance of hinged multi-body systems, particularly those involving more than two hinged floating bodies. This study aims to fill this gap in experimental data for hinged multi-body systems beyond two bodies. The rectangular box was chosen as the test model due to its stable hydrodynamic properties and ease of numerical modelling. Five identical boxes were prefabricated and subsequently tested in the pool in a sequence ranging from one to five boxes to capture the motion performance. Additionally, a numerical programme based on potential flow theory was developed for mutual validation with the experimental data. Firstly, the physical properties of each box were determined through equations calculation and a free decay test, enabling the acquisition of all parameters for conducting numerical simulations. Then, the response amplitude operator (RAO) curves for the heave and pitch motion of a single box were depicted, and the results indicated that the resonant frequency in pitch direction obtained from the regular wave test was consistent with that obtained from the free decay test. Finally, the motion RAO curves of hinged multi-body systems were presented and analysed. The agreement between the measured and computed results confirms the suitability of the experimental data presented in this study as benchmark data for validating numerical simulations.

Coupled Motion Response Analysis for Dynamic Target Salvage under Wave Action

The strategic recovery of buoys is a critical task in executing deep-sea research missions, as nations extend their exploration of marine territories. This study primarily investigates the dynamics of remotely operated vehicle (ROV)-assisted salvage operations for floating bodies during the recovery of dynamic maritime targets. It focuses on the hydrodynamic coefficients of dual floating bodies in this salvage process. The interaction dynamics of the twin floats are examined using parameters such as the kinematic response amplitude operator (RAO), added mass, damping coefficient, and mean drift force. During the “berthing stage”, when the double floats are at Fr = 0.15–0.18, their roll and yaw Response Amplitude Operators are diminished, resulting in smoother motion. Thus, the optimal berthing speed range for this stage is Fr = 0.15–0.18. During the “side-by-side phase”, the spacing between the ROV and FLOAT under wave action should be approximately 0.4 L to 0.5 L. The coupled motion of twin floating bodies under the influence of following waves can further enhance their stability. The ideal towing speed during the “towing phase” is Fr = 0.2. This research aims to analyze the mutual influence between two floating bodies under wave action. By simulating the coupled motion of dual dynamic targets, we more precisely assess the risks and challenges inherent in salvage operations, thus providing a scientific basis for the design and optimization of salvage strategies.

A study into the correlation between single array-hull configurations and wave spectrum for floating solar photovoltaic systems

Floating photovoltaic (FPV) systems offer a viable renewable energy solution due to easy installation and cost-effectiveness compared to other renewable energy generation methods. On the other hand, land-based solar photovoltaics face challenges such as space scarcity and environmental impacts. Shifting to nearshore locations unlocks vast ocean space potential, though waves expose significant challenges to FPV systems. Several novel FPV system designs are proposed, inspired by high-speed vessel multihulls, including catamaran, trimaran, quadrimaran, and pentamaran configurations, as floating supports for solar panels. Simulations were conducted to determine Response Amplitude Operators (RAOs) under various irregular wave spectrum conditions in a free-floating initial state. The FPV motion problem was solved using linear potential-flow theory with the Boundary Element Method (BEM) with Green-Function approach. Superposition of wave spectral energy and motion RAOs was used to obtain spectral structural responses. Motion in heave, roll, and pitch modes was evaluated across wave spectrum types. Results show that adding hulls reduces the significant amplitude response in all motion modes. In summary, valuable insights into floater designs and the hydrodynamic evaluation of FPV systems are presented.

Dynamic analysis of multi-module floating photovoltaic platforms with composite mooring system by considering tidal variation and platform configuration

Floating Photovoltaics (FPV) are emerging as an innovative technology to utilizing solar energy which advances the exploration of renewable energy technologies in the deep sea. This investigation proposes a novel methodology to verify the feasibility of the designed models in time-domain analysis via the motion responses, the mooring analysis based on the finite element method (FEM) and the airgap analysis, considering a comparison of dynamic responses between the regular hexagon shape and rectangle shape semi-submersible floating photovoltaic platform (FPVP) both combinate the cables and the tensioners mooring system to adapt the tidal variation. Initially, the response amplitude operators (RAOs) of the two configurations of the FPVP numerical models established in AQWA are derived from the frequency-domain analysis. Then, the method of rectifying the RAOs by incorporating additional damping essential to compensating the fluid viscosity due to the limitation of the potential flow theory is verified through comparison with the Computational Fluid Dynamics (CFD) solver. Subsequently, the motion responses of the two conceptualized FPVPs with the composite mooring system under different depths of water are assessed in time-domain analysis through OrcaFlex which regards the cables and tensioners as Morison type based on the FEM theory. Simultaneously, the variations in the air gap of platforms with dissimilar stiffness tensioners are compared to assess the safety of FPV systems under different water depths. The long-term extreme forecast of effective tension force for various return periods derived from the Weibull distribution model is verified. Finally, considering the factors that influence the design and safety of multi-module floating photovoltaics in variable-depth water, this study provides essential guidance for the safe construction technology of semi-submersible FPVPs, serves as a valuable reference for promoting reliable and cost-effective FPV technologies for offshore environments.

Numerical Investigation into the Hydrodynamic Performance of a Biodegradable Drifting Fish Aggregating Device

Drifting fish aggregating devices (DFADs) can significantly enhance fishing efficiency and capability. Conventional drifting devices are prone to degradation in harsh marine environments, leading to marine waste or pollution. In this study, we develop a biodegradable DFAD (Bio-DFAD) to minimise negative impacts on marine ecology. To investigate the hydrodynamic performance of the proposed device, numerical modelling involving the unsteady Reynolds-averaged Navier–Stokes equation has been conducted, in which a realisable k–ε model is applied to consider the turbulence effect. The response amplitude operators, which are key parameters for design, are obtained for heave and pitch motions. The hydrodynamic performance is found to be sensitive to the relative length, relative diameter, and wave steepness, but they are less sensitive to the relative current velocity. This work provides some scientific insights for practical applications.

Design and stability analysis of a new six-floater oscillating water column-based floating offshore wind turbine platform

The operational efficiency and lifespan of Floating Offshore Wind Turbines (FOWTs) are adversely impacted by the inherent platform motions and undesired vibrations induced by wind and wave loads. To effectively address these effects, the control of specific structural motions is of utmost importance, with platform pitch and yaw identified as the primary Degrees Of Freedom (DOF) that require attention. This study proposes a novel utilization of Oscillating Water Columns (OWCs) as a reliable and viable solution to mitigate platform pitch and yaw motions, thereby significantly enhancing the efficiency and reducing fatigue in wind turbines. This article aims to evaluate the impact resulting from integrating OWCs within each discrete floater of a Six-Floater platform. By considering different combinations of OWCs, a comprehensive analysis of the Response Amplitude Operators (RAOs) associated with pitch and yaw motions is presented. The primary objective is to identify the most efficient arrangements of OWCs and determine suitable combinations that effectively stabilize platform pitch and yaw motions. The empirical results substantiate that specific OWC configurations exhibit notable dampening effects on both pitch and yaw motions, particularly within specific wave frequency intervals. Consequently, it can be inferred that the integration and adequate operation of OWCs facilitate a substantial improvement in the stabilization of multi-floater platforms.

Numerical Estimation of Hydrostatic and Hydrodynamic Forces of Spar Type Offshore Wind Turbines

Abstract The focal point revolves around Floating Offshore Wind Turbines (FOWT) due to fossil fuel leakage. Numerical simulation tools have been developed to simulate the operational dynamics of FOWT under different wave conditions.In this study,a numerical approach is proposed to investigate FOWT using ANSYS-AQWA a commercial soft wares uses potential theory that employs the boundary element method to obtain the added mass, radiation damping and diffraction in three translational degrees of freedom (surge,sway,heave).in this study considers. This paper compares two numerical approaches for studying offshore structures. The first approach was conducted using WAMIT, and in this work, a verification of the with the well known Spar offshore wind turbine OC3 will be introduced. The heave response of FOWT will be considered in regular waves. Response Amplitude Operator (RAO) is considered in Heave Motion. The simulation achieves high accuracy with minimal errors, and its processing time is significantly shorter compared to CFD simulations.

Riser Configuration Design for a 15-MW Floating Offshore Wind Turbine Integrated with a Green Hydrogen Facility

Green hydrogen presents a sustainable and environmentally friendly solution for clean energy production and transportation. This study aims to identify the optimal profile of green hydrogen transportation risers originating from a floating offshore wind turbine (FOWT) integrated with a hydrogen production facility. Employing the Cummins equation, a fully coupled dynamic analysis for FOWT with a flexible riser was conducted, with the tower, mooring lines, and risers described using a lumped mass line model. Initially, motion response amplitude operators (RAOs) were compared with openly published results to validate the numerical model for the FOWT. Subsequently, a parametric study was conducted on the length of the buoyancy module section and the upper bare section of the riser by comparing the riser’s tension and bending moment. The results indicated that as the length of the buoyancy module increases, the maximum tension of the riser decreases, while it increases with the lengthening of the bare section. Furthermore, shorter buoyancy modules are expected to experience less fatigue damage, with the length of the bare section having a relatively minor impact on this phenomenon. Consequently, to ensure safety under extreme environmental conditions, both the upper bare section and the buoyancy module section should be relatively short.

A numerical study on a winglet floating breakwater: Enhancing wave dissipation performance

Box-type floating breakwaters (FBs), widely used for marine protection, face challenges in their wave dissipation capabilities. Although the effectiveness of the winglet-type floating breakwater in improving wave dissipation has been recognized, the specific mechanisms involved are not fully understood. This research presents an innovative winglet breakwater design, featuring three unique winglet configurations: 4-wings, Down-wings, and Up-wings. The study examines its performance against both regular and irregular waves using the Smooth Particle Hydrodynamics (SPH) method, taking into account factors such as the wave period, FB immersion depth, and FB relative density. Numerical simulations indicate a marked enhancement in wave dissipation for the FB equipped with four winglets compared to a baseline model without winglets. The Response Amplitude Operator (RAO) amplitude for the winglet-equipped FB is notably lower, approximately half that observed in the baseline scenario. Notably, the winglet FB's performance in irregular waves outperforms that in regular wave conditions. The insights gained from the design of these winglets provide significant contributions to practical engineering applications.

Enhancing Hydrodynamic Performance of Floating Breakwaters Using Wing Plates

Understanding the dynamic response of floating breakwaters to wave forces is essential for optimizing their design and improving coastal protection. The response amplitude operator serves as a key parameter in accurately predicting the structural response amplitudes at different frequencies and wave angles. By incorporating this knowledge, adjustments can be made to enhance the effectiveness of floating breakwaters. In this study, a comprehensive 3D model of the mooring system is developed to simulate its behavior under various wave and current conditions. The model takes into account critical design factors such as pontoon shapes, anchor types, placements, and configurations. Through simulations, valuable insights are obtained regarding the performance of the wing-plate floating breakwater mooring system across different operational settings. These findings contribute to the optimization of floating breakwaters and their ability to protect coastlines from wave impacts.

A quasi-static mooring analysis approach for berthed ships

The existing literature extensively explores the environmental loads experienced by moored ships, a process known as mooring analysis. In order to model this analysis realistically, it is necessary to consider a number of variables, including ships' equations of motion, response amplitude operators, and mooring equipment capabilities. However, port authorities may lack comprehensive ship data. This study introduces a quasi-static equilibrium-state search method for berthed ships. It needs just basic ship particulars data and mooring arrangement data of berth and ship. The method enables the determination of crucial information such as mooring line load distribution, rope tension, rope failure and equilibrium ship position. Its versatility across ships and ports makes it noteworthy. Various analyses conducted on the method produce results with mean absolute percentage error values ranging from 0.57% to 2.23%, which are deemed significant and meaningful. Furthermore, the mathematical model of the method, which is currently considered to have three degrees of freedom, is open to improvement. The method has the potential to contribute significantly to various aspects, including the tail effect, the pretension effect, and the analysis of ropes with different stiffness values and capabilities.

Oblique wave interaction with dual submerged oscillating buoy as WEC near a partially reflecting wall

The hydrodynamic performance of a submerged dual cylindrical wave energy converter (WEC) in front of a partially reflecting vertical wall is investigated within the framework of linear wave theory. The double cylinders are fully submerged and are constrained only in heave motion. The conversion of wave action into usable power occurs by the coordinated motion of two buoy systems viz. a power take-off mechanism (PTO). The numerical solution for the boundary value problem comprising of wave diffraction and radiation by submerged dual cylinders is obtained using the Boundary Element Method (BEM). The study is devoted to investigating the influence of various factors, the effect of cylinder dimensions, cylinder-cylinder spacing, partially reflecting wall-cylinder distance, angle of wave attack, and its submergence. The compelling results are presented by examining the heave force, surge force, response amplitude operator (RAO), damping factor, and particular interest in the WEC energy capture efficiency under distinct seawall reflections. The study reveals that there is an increase in the WEC efficiency by ≈12% in the case of a dual cylinder compared to a single cylinder. Besides, the amplification of the WEC efficiency is ≈78% for the case of a fully reflecting wall compared to the WEC in the open fluid domain. The present study will further help to understand the dynamics of WECs integrated into protecting shore structures such as breakwaters, groins, and seawalls.

Theoretical modeling of a bottom-raised oscillating surge wave energy converter structural loadings and power performances

This study presents theoretical formulations to evaluate the fundamental parameters and performance characteristics of a bottom-raised oscillating surge wave energy converter (OSWEC) device. Employing a flat plate assumption and potential flow formulation in elliptical coordinates, closed-form equations for the added mass, radiation damping, and excitation forces/torques in the relevant pitch-pitch and surge-pitch directions of motion are developed and used to calculate the system's response amplitude operator and the forces and moments acting on the foundation. The model is benchmarked against numerical simulations using WAMIT and WEC-Sim, showcasing excellent agreement. The sensitivity of plate thickness on the analytical hydrodynamic solutions is investigated over several thickness-to-width ratios ranging from 1:80 to 1:10. The results show that as the thickness of the benchmark OSWEC increases, the deviation of the analytical hydrodynamic coefficients from the numerical solutions grows from 3 % to 25 %. Differences in the excitation forces and torques, however, are contained within 12 %. While the flat plate assumption is a limitation of the proposed analytical model, the error is within a reasonable margin for use in the design space exploration phase before a higher-fidelity (and thus more computationally expensive) model is employed. A parametric study demonstrates the ability of the analytical model to quickly sweep over a domain of OSWEC dimensions, illustrating the analytical model's utility in the early phases of design.

Fully nonlinear wave interaction with 2D floating body including nonlinear sloshing tank

Two-dimensional fully-nonlinear numerical sloshing tank (FN-NST) simulation program is developed based on boundary element method (BEM), potential theory with artificial free-surface damping, and space-fixed (global) coordinate system. The free surface in sloshing tank is updated by the mixed Eulerian-Lagrangian (MEL) method with material node approach (Full Lagrangian approach). The developed potential-based nonlinear model was validated through comparisons with available experimental and CFD (computational fluid dynamics) results and they show good agreements. The nonlinear sloshing model is then further implemented in the fully nonlinear wave and floating-body simulation program to observe the effects of liquid sloshing motion. In the fully nonlinear program, the entire nonlinear fluid pressure is integrated over the instantaneous wetted body surface and position, which is subsequently compared with the corresponding linear theory and results. The second-order effects are also identified from the fully-nonlinear simulation. The floater Response Amplitude Operators (RAOs) for frozen- and liquid-cargo cases are also compared for various wave frequencies and amplitudes to better identify the role of liquid cargo in the stability of rotational motions. The effects of the vertical location of liquid tank and artificial free-surface damping are also investigated.

Experimental and numerical investigation on the hydroelastic response of barge and KVLCC2 ship

In this paper, the hydroelasticity of two segmented ship models (Barge and KVLCC2) is investigated by experimental and numerical methods. A two-way Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA) coupled method is adopted and further validated its accuracy against experimental results. The current approach emphasizes the overall convergence between two solvers, maintaining a strongly coupled manner to comprehensively address the fluid-structure interaction phenomenon, including the added mass effect. A series of experiments of a segmented Barge and KVLCC2 under various wave conditions were firstly conducted. The motions of the models are measured and the displacement Response Amplitude Operators (RAOs) are calculated. The CFD-FEA coupled method is demonstrated in agreement with experimental results by comparing the numerical prediction with the tank test results in terms of motion, affirming the validity and robustness. Finally, the hydroelastic response is discussed and investigated.

Exploring Motion Stability of a Novel Semi-Submersible Platform for Offshore Wind Turbines

The stability of offshore floating wind turbine foundation platforms is a fundamental requirement for the efficiency and safety of wind power generation systems. This paper proposes a novel small-diameter float-type semi-submersible platform to improve system stability. To evaluate the superior motion stability of the proposed floating platform, a comprehensive frequency–domain response analysis and experimental study were conducted in comparison with the OC4-DeepCwind platform developed by the National Renewable Energy Laboratory (NREL). The respective comparison of the frequency–domain response analysis and the experimental results demonstrated that the proposed floating wind turbine platform shows better hydrodynamic characteristics and resonance avoidance capability. This not only reduces the Response Amplitude Operators (RAOs), but also enhances the system stability, namely, effectively avoiding the regions of concentrated wave loading and low-frequency ranges. Furthermore, the proposed small-diameter semi-submersible platform has the potential to reduce manufacturing costs, providing valuable insights for the manufacturing of offshore floating wind turbine systems.

Data-driven method for hydrodynamic model estimation applied to an unmanned surface vehicle

Unmanned surface vehicles (USVs) are increasingly appealing for gathering metocean data, including directional sea spectra. This paper presents new developments towards estimating the response amplitude operators (RAOs) of surface vehicles equipped with inertial sensors. The novel approach undertakes the data-driven estimation of vehicle models of the wave-induced heave, roll, and pitch motion dynamics, as required to perform subsequent seakeeping computations. Specifically, a genetic algorithm executes the calibration of available closed-form RAOs for a simplified geometry. The algorithm makes a population of model-fitting parameters evolve towards minimising discrepancies between the predicted and measured response spectra in stationary operational conditions. Trust in the model is eventually increased by screening and merging the best-fitting solutions. Resulting response predictions using high-resolution spectral wave data for the AutoNaut USV demonstrate satisfactory accuracy and robustness in heave and pitch but a worse fidelity in roll, thereby motivating follow-up studies to improve the estimation of roll RAOs.

Evaluation of an experimental kelp farm’s structural behavior using regression modelling and response amplitude operators derived from in situ measurements

An experimental kelp farming system for exposed ocean conditions was designed, deployed, planted with kelp and instrumented for evaluation of its dynamic response to ocean waves, tides, and currents. The farm featured a novel “lattice” mooring design and anchor lines and cultivation lines (horizontal lines used as kelp growth substrate) made of fiberglass rods. The farm was deployed at a site in Saco Bay, Maine with 13 m (MLLW) water depth. There the farm was exposed to waves with heights up to 5.9 m. Anchor line tension, tide and wave height time series were gathered and processed into response amplitude operators (RAOs) and least squared error linear regression models enabling recognition of meaningful patterns between the forcing factors and the mooring response. Mean mooring line tensions were shown to increase nonlinearly with tide. Anchor line tension response amplitudes were shown to exhibit high sensitivity to both low and high frequency wave forcing. Numerical free-release test simulations suggested natural frequencies in heave of 0.91 Hz, indicating that tension response sensitivities at high frequency could be the result of resonance. Low frequency tension response disproportionate to the low frequency wave forcing could be explained by wave forcing on kelp cultivation arrays modulated by wave group envelopes. Instances of high magnitude, potentially damaging peak tensions, deemed shock loads, were prevalent in most load cases. Anchor line tension dynamics including RAO and shock load magnitudes were shown to be sensitive to mooring stiffness (ratio of tension to resulting elongation) and, in some cases, significant wave amplitude. Patterns of anchor line response indicated that additional mooring elasticity or geometric compliance and use of floatation with less sensitivity to high frequency waves could help avoid the cause of and costly consequences of amplified high frequency loading and high amplitude shock loading. RAOs and regression model results also indicated a subdued response in frequencies associated with ocean swell waves, suggesting desirable performance in waves most dominant in extreme storm events. With the proposed improvements, the farm system design suggests merit as a robust and durable macroalgae biomass production platform.

Investigation of Seakeeping Performance of Trawler by the Influence of the Principal Particulars of Ships in the Bering Sea

Investigating ship motion under real conditions is vital for evaluating the seakeeping performance, particularly in the design process stage. This study examined the influence of the principal particulars of a trawler on its seakeeping performance. The wave conditions in the Bering Sea are investigated using available data. The length-to-beam (L/B) and beam-to-draft (B/T) ratios of the ship are changed by 10% for the numerical simulation. The response amplitude operator (RAO) motion, root mean square (RMS) value and sensitivity analysis are calculated to evaluate the influence of the trawler dimensions on ship motions. The peak RAO motion affected the ship motions noticeably because of the resonance at the natural frequency. The L/B and B/T ratios are important geometric parameters of a ship that significantly influence its RMS motion, particularly in the case of roll and pitch. The change in the B/T ratio has a good seakeeping performance based on a comparison of the roll and pitch with the seakeeping criteria. The present results provide insights into the seakeeping performance of ships due to the influence of the principal dimensions in the design stage.

Hydrodynamic Responses of Heaving Motion on One Body and Two Body Point Absorber Devices with Different Wave Condition in Malaysia

Wave energy harvesters are still not as mature as other types of renewable energy harvesting devices, particularly when it comes to commercialization, mass production, and grid integration, even though ocean waves around the world are known to contain high and dense quantities of energy. However, recent studies and optimizations suggested that the point absorber wave energy harvester may be a viable option. This paper provides a comprehensive comparison hydrodynamic damping analysis of the heaving motion on one body and two body point absorber wave energy harvesters by using Computational Fluid Dynamic (CFD) software. A simulation run was proposed for the analysis performance of damping of the point absorber devices to low wave height (0.7m-2.5m) and period (0.9s-2.2s). There are two types of point absorbers: one-body point absorber and two body point absorber. Both point absorber body are examined by simulation in terms of its heaving dynamic motion frequency in calm, medium and strong wave condition. This analysis highlights the extensive research being done to bring point absorbers closer to technical maturity, paving the way for commercialization and mass production for low wave characteristics. The results showed two body point absorber Response Amplitude Operator (RAO) is improved to absorbed low wave height compared to one body by RAO efficiency 17% and device efficiency 25%. The two-body point absorber performed better in all wave condition.