Heave Motion Research Articles

Modelling Sea-Surface Wave Motion and Ship Response Using Smoothed Particle Hydrodynamics and Finite Element Analysis

The response of a ship or other vessel to surface sea waves, including extreme waves, may compromise crew and vessel safety and long-term operational capability. Herein, a novel high-fidelity numerical time-dependent simulation approach is presented using Smoothed Particle Hydrodynamics (SPH) for modelling sea waves coupled with Finite Element Analysis for modelling vessel structural response under wave loading conditions. The results are compared with physical scale model wave tank test results. Good agreement was obtained for heave and pitch motions and vertical bending moments for various forward (head) speeds in regular head waves, heave and pitch motions, and vertical bending moments. High computational demands can be met by the increasing availability of computation power. Ongoing research is outlined. The implications for the design of vessels such as ships and for through-life assessment are discussed.

Assessment of ADIS 16364 for the Examination of Ship Motions in the Free-Running Model

The ADIS 16364 instrument is frequently employed for direct measurement of ship motion on ships. However, the validation process for ADIS 16364, to assure its reliability in monitoring ship motion, has not yet been completed. The ship motion model test conducted at the hydrodynamics laboratory utilizes the free-running test technique in conjunction with the QUALISYS motion capture system and the ADIS 16364 device. The purpose of this assessment is to ascertain the instrument's appropriateness for performing ship motion testing. The ADIS device is composed of two components: an accelerometer and a gyroscope. These components are employed to quantify the acceleration of the ship's heave motion and the rotational velocity of its pitch and roll motions, respectively. Utilizing a motion capture system, the QUALISYS Motion Capture System records the motion of a ship model. The examination evaluates two discrete waves produced, comprising two cases of regular waves measuring 10 centimetres in height and 1.5 seconds in period and two cases of irregular waves measuring 16 centimetres in height and 1.75 seconds in period. The elevation motion data in the time domain is acquired from the measurements of the instrument via a wireless system. Following this, various numerical processing methods are implemented, including the moving average filter and cumulative trapezoidal numerical integration. As a result, the root mean square percentage error (RMSPE) discrepancies between the two measuring instruments for regular waves are restricted to a maximum of 5.7% for roll motion and fall below 4% for heave and pitch motions. In the results of the model test response, every movement in both the regular wave and irregular wave scenarios is the same because it does not have an RMSPE of more than 5%.

Fully Coupled Analysis of a 10 MW Floating Wind Turbine Integrated with Multiple Wave Energy Converters for Joint Wind and Wave Utilization

The study focuses on a semi-submersible wind-wave integrated power-generation platform, which consists of an OO-Star semi-submersible platform equipped with a DTU 10 MW wind turbine and a set of wave energy converters. A hydrodynamic model was established using ANSYS-AQWA (2023 R1), and by incorporating upper wind loads and utilizing the open-source program F2A, a fully coupled time-domain model of the integrated power-generation platform was constructed. The primary objective is to explore the interaction mechanisms between the upper wind turbine and the lower wave energy devices under the combined effects of irregular waves and turbulent wind through a series of operational conditions. Additionally, the safety of the mooring system was assessed. The results indicate that, compared to the wave period, the power generation of the lower wave energy devices is more significantly affected by wave height. Overall, the integrated power-generation platform demonstrates optimal performance under the third operational condition. In survival conditions, the introduction of oscillating buoys can improve the motion responses of the platform in terms of sway, roll, pitch, and yaw to a certain extent, but it also increases the surge and heave motion responses and the associated mooring loads. The mooring system can ensure the safety of the integrated power-generation platform under extreme sea conditions.

Nonlinear harmonic resonant behaviors and bifurcation in a Two Degree-of-Freedom Duffing oscillator coupled system of Tension Leg Platform type Floating Offshore Wind Turbine

The surge-heave coupled motion model of a Tension Leg Platform type Floating Offshore Wind Turbine (TLP FOWT) is first established. By taking the tendons stretching and platform set-down motion into consideration, the nonlinear model is a Duffing oscillator coupled system. We analyze the nonlinear feature in the surge-heave coupled motions by the semi-analytical algorithms in nonlinear dynamics. The harmonic balance method is applied to obtain the analytical solutions of the nonlinear system under wind and wave excitations. The analytical solution verifies the excellent accuracy. To further achieve the heave motion response, we organize the bifurcation analysis and discuss the effects of the dynamic parameters on the heave responses. The results reveal the multi components of heave motion, which consist of constant, primary harmonic resonate and higher order harmonic resonate. In addition, the change of dynamic parameters has various effects on the response. The increment of wave load leads to the expansion of heave response, and an instantaneous expansion appear. Both linear surge and heave damping only affect the amplitudes of heave motion. The nonlinear surge stiffness and heave stiffness can barely affect the primary harmonic resonance amplitudes, but they present different effects on the higher order harmonic resonance component.

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.

Hydrodynamic performance characteristics of small-scale in-situ buoys with critical motion requirements

As the accuracy of high-precision oceanographic measurement instruments increases, the operational requirements for buoy motion become critical. This study focuses on the small-scale in-situ buoy, optimizing buoy configuration to ensure stability and performance. Aiming at the special structure which consists of a large floating column and several small tube connectors, a method for evaluating the hydrodynamic performance is proposed which combines potential flow theory with Morison equation. And the method validity is confirmed using experimental data. The performances analysis of different type buoy with catenary or taut mooring system are developed. According to the critical motion requirements for the long-term stability, the cylindrical type buoy equipped with a catenary mooring system is regarded as the most stable and economical choice, exhibiting a surge motion response of 4.07 m, a heave motion response of 2.89 m, and a pitch motion response of 9.37°. Furthermore, the anchor chain acts as an elastic damper which can mitigate the transient impact of the environmental loads, greatly limiting the amplitude of the longitudinal and heaving motions. And the maximum mooring line tension is 249.28 kN, which is significantly lower than other schemes. The evaluation method offers a technical support for engineering applications.

Prediction of energy harvesting efficiency through a wake–foil interaction model for oscillating foil arrays

This research investigates the wake–foil interactions between two oscillating foils in a tandem configuration undergoing energy harvesting kinematics. Oscillating foils have been shown to extract hydrokinetic energy from free-stream flows through a combination of periodic heave and pitch motions, at relatively higher amplitudes and lower reduced frequency than thrust generating foils. When placed in tandem, the wake–foil interactions can govern the energy harvesting efficiency of the system due to a reduced relative flow velocity in combination with a structured and coherent wake of vortices shed from the high amplitude flapping of upstream foils. This work utilizes simulations of two tandem foils to parameterize and model the energy harvesting performance as a function of array configuration and foil kinematics. Once the wake of the leading foil has been fully parameterized, the placement, phase angle and kinematic stroke of the second foil is utilized to estimate the time-dependent power curve. The algorithm predicts the power of the second foil through the mean and unsteady wake characteristics, including the direct impingement of a vortex with the trailing foil.

Experimental study on hydrodynamic performance of the semi-submersible vessel-shaped fish cage

Deep-sea net cages play a vital role in expanding offshore farming in modern marine fisheries. In this paper, a model-scale 1:40 tank experiment was conducted for a vessel-shaped truss-structured single-point mooring deep-sea aquaculture net cage. The study focused on the hydrodynamic characteristics, including the effect of current, wave, and net on the mooring force, heave, and pitch motion behaviors. Experimental results indicate that the mooring force increases with the current velocity, draught of the cage, and wave height, but decreases with the wave period increase. Both heave and pitch movements amplitudes increase with wave height. While heave motion amplitude initially declines and then ascends with wave periods, pitch motion shows the opposite pattern. Besides the net has an obvious damping effect on the pitch motion. These results can provide data support for the design and offshore installation of vessel-shaped truss-structured net cages in the future.

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.

Exploiting Axisymmetry to Optimize CFD Simulations—Heave Motion and Wave Radiation of a Spherical Buoy

Simulating the free decay motion and wave radiation from a heaving semi-submerged sphere poses significant computational challenges due to its three-dimensional complexity. By leveraging axisymmetry, we reduce the problem to a two-dimensional simulation, significantly decreasing computational demands while maintaining accuracy. In this paper, we exploit axisymmetry to perform a large ensemble of Computational Fluid Dynamics (CFDs) simulations, aiming to evaluate and maximize both accuracy and efficiency, using the Reynolds Averaged Navier–Stokes (RANS) solver interFOAM, in the opensource finite volume CFD software OpenFOAM. Validated against highly accurate experimental data, extensive parametric studies are conducted, previously limited by computational constraints, which facilitate the refinement of simulation setups. More than 50 iterations of the same heaving sphere simulation are performed, informing efficient trade-offs between computational cost and accuracy across various simulation parameters and mesh configurations. Ultimately, by employing axisymmetry, this research contributes to the development of more accurate and efficient numerical modeling in ocean engineering.

Virtual prototype modeling and fuzzy control of the heave compensation system for a 500-ton deep-sea mining vessel

The unexpected heave motion of vessels generated by waves has always threatened the safe operation of mining vessels. The heave compensation system is a critical equipment for offshore cranes to ensure the safety and stability of the deep-sea mining vessel operation. Unfortunately, the nominal load of the mining vessel transporting minerals has become increasingly large, which has led to the dynamic performance of the heave compensation decline and a significant increase in energy consumption. To solve these problems, a semiactive heave compensation system and fuzzy logic-based controller are proposed in this paper. First, an active-passive hybrid heave compensation system is designed to reduce energy consumption greatly. The virtual prototype models of the proposed heave compensation system in a 500-ton deep-sea mining vessel are also built. Then, an adaptive tuning PID controller is developed based on the Transfer function of the heave compensation system and Mamdani-type fuzzy logic. Virtual prototype simulation results of AMESim-Simulink joint simulation illustrate that the accuracy of compensation for the four or six sea states reaches more than 90% with the proposed method and the power of the active compensation system is about 21% of the total power. Finally, the experimental results are included to demonstrate the effectiveness of the proposed semiactive heave compensation system.

Multi-step prediction of ship heave motion using transformer-enhanced multi-scale CNN

To achieve precise multi-step heave motion prediction for active compensation control in marine equipment, an innovative approach that integrates an attention-fused multi-scale CNN with a Transformer encoder is introduced in this study. The dual-path CNN and point-wise convolution-enhanced Transformer encoder are designed to capture local features across various scales and the global characteristics of heave motion signals, respectively. Furthermore, a novel optimization objective which combines a slope factor-optimized Huber loss function with a maximum square distance loss function is proposed to better approximate the original signals at extreme points. The proposed model is trained and tested on simulated data under multiple sea conditions. In typical active compensation scenarios (Hs=3.5m), the proposed model demonstrates superior performance compared to baseline methods, achieving an RMSE of 0.0083 m, an MAE of 0.0066 m, and the upper whisker of the box plot for the prediction error is less than 0.02 m. These outcomes effectively satisfy the accuracy requirements for active compensation systems. The generalization test on real-ship collected data demonstrates excellent performance after fine-tuning. Additionally, the model is considered suitable for deployment in real-world applications due to its memory efficiency and fast inference speed.

Experimental Investigation of the Heaving Motion Effect on Critical Heat Flux Phenomena and Wall Temperature Fluctuation Using R134a for Floating Nuclear Applications

This study experimentally investigated the flow boiling critical heat flux (CHF) under heaving conditions pertinent to floating nuclear power plants (FNPPs). Experiments were conducted using R134a to simulate the operational pressure of pressurized water reactors, extending the CHF database to a pressure range of 5 to 18 MPa. The tested heaving motion reached up to 0.6 g of maximum acceleration, with a period that varied from 3 to 5.3 s. A parametric trend involving mass flux, critical quality, and motion conditions was analyzed through extensive tests encompassing static and heaving conditions. The results showed that CHF reduction was observed due to the effect of heaving acceleration, even in the absence of oscillations in other thermal-hydraulic factors. The CHF reduction was up to 9% in the present experimental conditions. The heaving motion effect was prominent under two specific thermal-hydraulic conditions: when the critical quality was close to zero and when it exceeded the value of 0.6. Furthermore, an examination of wall temperature responses suggested that a longer period of heaving motion can lead to an earlier occurrence of CHF. This fundamental effort was conducted to enhance the understanding of the CHF mechanism under motion conditions, with the aim of contributing to the safe and efficient design of FNPPs.

Power absorption and flow-field characteristics analysis for oscillating coaxial twin-buoy wave energy converter by using CFD

The energy conversion capacity of wave energy conversion devices highly depends on the hydrodynamic characteristics of the energy-harvesting structure. To investigate the effect of hydrodynamic performance on the power conversion characteristics, a twin-buoy wave energy converter (WEC) was investigated by using a three-dimensional numerical wave pool based on the Computational Fluid Dynamics (CFD) method. Several factors are examined, including the elasticity coefficient of the anchor chain, the bottom configuration of the floating body, and the power take-off (PTO) damping coefficient. The heave displacement, heave velocity, and heave force of the converter are calculated under specific wave parameters, and the flow field cloud diagram during the heave motion is analyzed. The results indicate that a wave energy converter with a hemispherical floating body exhibits the best kinematic performance. The influence of the mechanical damping coefficient on the energy conversion performance of the device is studied. By appropriately reducing the mechanical damping coefficient, the energy capturing capability of the device can be increased to a certain extent. These findings can serve as a theoretical basis for the application of deep-water wave energy conversion in engineering and the optimization of future WEC designs.

Numerical study on hydrodynamic interaction between two parallel surge-released ships advancing in head regular waves based on the hybrid method

This study examines the hydrodynamic interaction between two parallel surge-released ships in head regular waves. A hybrid approach combining potential flow theory and functional-decomposition URANS is used for an efficient and accurate simulation. The methodology involves a surge-released module, 4DOF motion equations, multiple coordinate systems, and a dynamic structured grid. Two ship models are used for validation, comparing numerical and experimental results in ship motions and wave loads. The analysis shows good agreement, with differences of less than 5 % in heave and pitch motions, less than 8 % in roll motions, and less than 15 % in total resistance and sway interference forces. Present study also observes consistent trajectories of the wave system between the two ships. The influence of surge motion and wave height on wave-ship-ship interaction is investigated, emphasizing the importance of considering surge motion in seakeeping performance and longitudinal separation. The occurrence of parametric roll in Ship B is accurately resolved by the hybrid method and the parametric roll amplitude is smaller under ship-to-ship interaction conditions. Wave-induced moments play a limited role in this phenomenon, while the dominating roll restoring moment exhibits a hardening effect. Accordingly, roll motion and moments remain relatively unchanged with increasing wave height, indicating the strong nonlinear nature of parametric roll.

Hydrodynamic Analysis of Different Formation Configurations of Catamaran in Regular Head Waves

When undertaking long-distance missions at sea, vessels aim to achieve an extended operational range through drag reduction and energy efficiency, while enhanced wave resilience also provides substantial benefits. In this work, the Delft-372 catamaran is utilized to investigate the feasibility of drag reduction and roll mitigation for catamaran formation sailing in waves, analyzing the effects of three different formation configurations and varying spacings. The overset grid method was employed to simulate vessel motions, while the Volume of Fluid (VOF) method captured the free surface. First, the numerical results of the catamaran’s resistance, pitch, and heave motion amplitudes under different wave conditions were compared with experimental data to verify the accuracy of the CFD numerical method, and a grid convergence analysis was performed. Next, numerical models of the Delft-372 catamaran were constructed in parallel, tandem, and lateral formations under wave conditions. The results of the single-ship simulation were employed as a benchmark to analyze the impact of different formation configurations and varying lateral and longitudinal spacings on the resistance, pitch, and heave motions of the catamarans. The study also examined the effects of wave interference between vessels and the combined influence of external waves on individual and overall hydrodynamic performance. Results indicated that the tandem formation outperformed the parallel and lateral formations, with optimal performance observed at the longitudinal distance of 1 LPP. Generally, during navigation, the follower catamaran should ideally be positioned in the trough of the stern wave of the leader catamaran.

Coupling Analysis between the Transonic Buffeting Flow and a Heaving Supercritical Airfoil Based on Dynamic Mode Decomposition

The coupling between a transonic buffeting flow and a supercritical airfoil with harmonic heave motion was studied. A parametric space of the heave frequency and amplitude was investigated using a verified fluid–structural interaction framework. The spatial-temporal flow pattern around the transonic airfoil was studied using dynamic mode decomposition (DMD) to unveil the physical coupling mechanism. The results show three types of flow responses under the heave motion: (I) A buffet frequency response with a λ-shape shock wave structure and recirculation zone at the shock foot. The aerodynamic performance was alike the scenario in the flow past the stationary airfoil. (II) A transitional response with a weakened shock and enhanced boundary layer. The aerodynamic performance deteriorated sharply at f=fbuffet and recovered after the frequency was past the buffet frequency. The flow pattern was characterized by a double-shock structure that interacted with the enhanced boundary layer. (III) A heave frequency response with the dominant heave motion. The variance in the aerodynamic loading increased significantly at f>fbuffet and there were higher heave amplitudes in this stage. The driving motion of the airfoil transferred the energy of the buffet mode to the boundary layer with a more even energy balance according to the energy contribution analysis of the DMD modes.

On the role of wake-capture and resonance in spanwise-flexible flapping wings in tandem

Numerical simulations of the flow around spanwise-flexible flapping wings in tandem are reported, focusing on a thrust-generating configuration. Wings of aspect ratio 2 and 4 in forward flight undergo heaving and pitching motion following optimal 2D kinematics. The Reynolds number of the simulations is Re=1000. The effect of flexibility is explored by varying the effective stiffness of the wings, while the effective inertia is kept constant. The aerodynamic performance of the tandem system results from a combination of unsteady aerodynamics mechanisms, fluid–structure resonance, vortex–wing interactions (denoted wake capture in this study) and aerodynamic tailoring. It is found that the aerodynamic performance and structural behavior of forewings are dominated by a fluid–structural resonance. The maximum mean thrust for the forewings is obtained when the driving frequency approaches the first natural frequency of the structure, ωn,f/ω≈1, similarly to what is observed in isolated wings undergoing the same kinematics. On the other hand, hindwings show optimal performance in a broad region near ωn,f/ω≈2, and their aerodynamic performance seems to be dominated by wake–capture and aerodynamic–tailoring effects. The aerodynamic performance of the hindwings is dependent on the flexibility of the forewing, which impacts the intensity of the vortices shed into the wake and the resulting effective angle of attack (i.e., wake capture). The timing between the effective angle of attack and the pitching motion of the hindwing controls the generation of thrust (or drag) of each spanwise section of the hindwing (i.e., aerodynamic tayloring). A proof of concept study on the aerodynamic performance of systems made of wings with different flexibility suggests that they could outperform tandem systems with equally flexible wings. Thus, the optimal mixed–flexibility tandem system is composed by a resonant forewing, which maximizes the thrust generation of the forewing and the intensity of the vortices shed into the wake, and a hindwing whose flexibility must be tuned to maximize wake capture effects.

Study on aerodynamic and coupled motion response characteristics of floating vertical axis wind turbine

ABSTRACT To improve the efficiency of a floating VAWT (FVAWT), the aerodynamic and coupled motion response characteristics of 5MW Φ-type FVAWT are studied in fully coupled system. Based on the computational fluid dynamics (CFD) method, the dynamic fluid body interaction (DFBI), overlapping grid and dynamic mesh technique are adopted for numerical simulations. Under wind-wave coupling conditions, the power coefficient (Cp) and motion response of FVAWTs with different tip speed ratios (TSR) and height-todiameter ratios (η) are analysed. The mechanism of platform heave motion on torque Q generation of VAWT is explored. The results show that the FVAWT with height-to-diameter ratio of 1.2 and tip speed ratio of 5 has optimal aerodynamic and motion performance. Under the optimal tip speed ratio, the Cp of the offshore FVAWT is 5.21% higher than that of the land VAWT. As the floating platform rises, the torque of wind turbine decreased correspondingly, and vice versa.

Ditching characteristics of a seaplane under various wave conditions and effects of biomimetic floats

This paper presents a numerical investigation into the hydrodynamic loads and motions experienced by two seaplane models during ditching in calm water and regular waves. The original bare model is susceptible to jet flows and wave overwash at the nose, which can adversely impact the aircraft's ditching performance. To address these issues, we introduced two biomimetic floats symmetrically to the original model and assessed their influence on the ditching dynamics. A comparative analysis was conducted on the accelerations, impact loads, and the coupled heave and pitch motions of both the original and the redesigned model equipped with floats during ditching in both calm waters and regular waves. For the wave ditching scenario, a detailed investigation of the slamming phase was first carried out, involving impacts at the wave's zero-crossing, crest, and trough. The cases with a variety of wave heights, wave lengths, and wave headings were evaluated. A particular focus was placed on understanding how the biomimetic floats affect the seaplane's performance during ditching in both calm and wavy conditions. The analysis of maximum accelerations and pitch angles during wave ditching revealed that slamming at the wave trough presents the most significant hazards. Additionally, the phenomena of gliding and wave overwash were identified as substantial risks under wave conditions. The results suggested that the biomimetic floats can effectively mitigate the maximum horizontal acceleration and pitch angle of the original model, enhancing the safety of ditching operations in both calm water and waves.