Motion Response Amplitude Operators Research Articles

Numerical Study of the Hydrodynamic Response of Biodegradable Drifting Fish Aggregating Devices in Regular Waves

Fish-aggregating devices play a significant role in tuna purse fisheries. The severe marine environment and the large number of non-biodegradable fish-aggregating devices impact structural safety and cause marine litter. Therefore, hydrodynamic performance and the use of biodegradable materials are crucial issues for ensuring the sustainability of fish-aggregating devices. In this study, a type of virtual biodegradable drifting fish-aggregating device (Bio-DFAD) was designed. Numerical simulations were conducted to investigate the motion responses and relative velocities of Bio-DFADs in regular waves (first- and fifth-order waves). The numerical model was applied based on unsteady Reynolds-averaged Navier–Stokes equations with the realizable k–ε model. For different scenarios of modeling, various conditions were modeled, including the relative length, wave steepness, and diameter of the balsa wood, to analyze their effects on the hydrodynamic response of the Bio-DFADs. The results indicated that the increased relative length, wave steepness, and diameter of balsa wood had a significant influence on the motion response amplitude operators (RAOs) and relative velocity of Bio-DFADs. The results suggested that a relative length (LF/B = 1.5) and smaller diameter (DF = 30 mm) were recommended for fewer motion responses and relative velocity. The obtained results provide insight for practical engineering applications of the hydrodynamic design of Bio-DFADs.

A floating system integrating a wind turbine with a steel fish farming cage: Experimental validation of the hydrodynamic model

This paper is dedicated to comparing the numerical results of the dynamic responses of a floating offshore wind turbine integrated with a steel fish farming cage (FOWT-SFFC) under wind and waves against the experimental data. FOWT-SFFC's numerical model is built with OrcaFlex where the potential flow theory and quadratic drag formula are used to calculate the hydrodynamic loads on the structural components of the floater, while Morison-type formulation is employed to model the force on fish nets. The numerical model is tuned in terms of the measured data. The simulated motion response amplitude operators and stochastic responses under irregular waves are compared with the experimental results to fathom the influence of drag's modeling on the simulation outcome. The effects of additional damping and 2nd-order wave forces are also investigated to determine the optimal simulation method. With the selected numerical model, the responses of FOWT-SFFC with and without nets under 100-year extreme waves, combined wind and irregular waves are calculated. The simulated response time histories, spectra and statistics are in good agreement with the experimental data. Besides, it is revealed that the effects of 2nd-order wave forces are important for the accurate simulation of low-frequency pitch motion, but unfavorable to the prediction of other responses.

A Numerical Study on the Performance of the 66k DWT Bulk Carrier in Regular and Irregular Waves

Accurate resistance performance evaluation is essential to predict the minimum propulsion horsepower required for ships in real sea. Therefore, in this paper, the added resistance performance of K-Supramax in various wave conditions was calculated using CFD (Computational Fluid Dynamics). First, to compare the resistance performance according to the DOF (Degree of Freedom), the added resistance performance in the head regular wave was investigated and compared with the experiment. The 2DOF and 6DOF results in the head regular wave had no significant differences. Second, to compare the resistance performance among various wave conditions, the effect of the heading angle was analyzed by comparing resistance and motion RAOs (Response Amplitude Operators) in bow quartering sea conditions using 6DOF. The added resistance showed the highest value near the resonance frequency of 170°. As the heading angle increased, the added resistance tended to decrease, regardless of the wavelength ratio. Also, the added resistance performance in irregular waves was investigated with reference to the adverse conditions. The spectral method, which linearly superimposes regular wave results, and the added resistance generated during irregular waves directly through CFD were compared. The resistance in irregular waves increased by approximately 92% for the spectral method and by approximately 72% for the direct irregular wave calculation compared to the resistance in calm water. In addition, the PSD (Power Spectral Density) of resistance and the distribution of motion RAOs obtained from direct irregular wave calculations were investigated.

A Numerical Study on the Hydrodynamic Performance of a Tanker in Bow Sea Conditions Depending on Restraint Conditions

The importance of accurate ship performance estimation is increasing for efficient ship operation. Ship performance has been evaluated through model tests in the past, but there are limitations in terms of facilities and costs. With the spread of high-performance computers, the method of evaluating the performance of a ship by numerical analysis, especially computational fluid dynamics (CFD), has become common. There have been many numerical studies on added resistance under various wave conditions for many years, showing a high reliability. Meanwhile, most of the studies were conducted under conditions where the degree of freedom (DOF) of the ship was limited due to computational complexity. In this study, we tried to compare the added resistance performance and fluid dynamics of S-VLCC with 6 DOFs in the regular wave conditions. One of the methods for utilizing the 6 DOFs is the soft-mooring system, which allows springs to be attached to the bow and stern to recover the non-restoring force of the hull. The second method considers the free-running condition. The virtual disk is used for the self-propulsion of the ship, and the rudder can be rotated to maintain its course. The propeller rotation speed and rudder angle are controlled through PID control. The bow wave (ψ = 180°) and oblique wave (ψ = 150°, 120°) conditions were considered, and various regular wave conditions from short to long wavelengths were regarded. The effects of restraint conditions on the added resistance and motion response amplitude operator (RAO), according to each wave condition, were compared. As a result, there was a difference in the roll motion for each restraint condition, and the y-direction force and yaw moment generated on the hull were compared to analyze the cause. In addition, we observed the change in flow characteristics by comparing the streamlines around the hull and the nominal wake on the propeller plane.

Numerical study on mean wave drift forces and moment of ships using Rankine panel method in frequency domain

A three-dimensional frequency-domain seakeeping model based on the Rankine panel method is developed to compute the mean wave drift forces and moment acting on ships with forward speeds. Two different linearization models (the double-body and Neumann–Kelvin models) are applied to evaluate the mean wave drift forces and moment using a near-field method. In these models, the Rayleigh’s artificial friction is adopted in the free-surface boundary condition to suppress longer wave components in computational regions apart from the ship. A novel upwind difference scheme is introduced to calculate the first-order and second-order derivatives of the velocity potential on the free surface. Wigley I, Wigley III and S175 containership are adopted in numerical simulations to validate the effectiveness of the developed model. In the present study, the motion response amplitude operators in head, beam and oblique seas obtained using the two models are compared, and their contributions to the mean wave drift forces and moment are analyzed. Results show that in head seas, the pitch motions have significant effects on the surge-directional wave drift force Fx. In beam seas, the heave motions have the most effect on the mean wave drift forces and moment (Fx, Fy and Mz).

CFD-Modified Potential Simulation on Seakeeping Performance of a Barge

This study proposes a computational fluid dynamics (CFD)-modified potential (CMP) model. This hybrid model uses linear potential theory with a corrected damping ratio obtained from CFD simulations to analyze the seakeeping performance of a small vessel. According to the analysis procedure of the proposed model, a motion analysis, including the prediction of the roll and pitch damping ratio of a small barge, was conducted; to verify reliability; the results were compared to those of an experiment performed in a physical tank. The relative errors in the experiment for peak amplitude in the roll motion response amplitude operators (RAOs) using the CMP model were relatively small, whereas those obtained from only the potential analysis were large errors in all three conventionally used roll-damping ratios. In addition, the computational time consumed by the CMP model was longer than that consumed by the potential theory but faster than the full CFD simulation for all wave conditions. Subsequently, based on the motion analysis results, the seakeeping performance was evaluated in a real sea environment, and the results on the single significant amplitude (SSA) were discussed through comparison with the results of the potential analysis and experiment.

Numerical and experimental study on the influence of a moonpool on motion performance and stability of a drillship

The existence of a moonpool may affect motion characteristics and stability of a drillship. This paper presents numerical and experimental study on the influence of the configuration of a moonpool on the motion performance and stability of a drillship under the condition of a constant displacement. Ship hydrostatics and three-dimensional (3D) potential flow theory are employed to calculate the static stability curves (GZ curves) and motion response amplitude operators (RAOs) of the drillship with conjoined double moonpools, separated double moonpools and single rectangular moonpools, respectively. Numerical model is validated by sea-keeping model tests of the drillship with a conjoined double moonpool carried out in towing tank. It is found that there is a critical heeling angle for the static stability curve of the drillship. The variation of the opening size of the moonpool is found to merely have significant effect on the heave RAOs of the drillship near the piston mode resonance period, while slightly influence on the pitch RAOs near the sloshing mode resonance period. It is demonstrated that smaller or larger openings of the moonpool under a constant displacement can reduce dramatically roll RAOs of the drillship around the natural roll period under bow quartering waves and beam waves, respectively. The coupling effect of roll and heave leading to the heave RAOs decreasing around the natural roll period in beam waves, as well as coupling effect in heave, pitch and roll motion RAOs around the natural roll period in bow quartering waves are observed in the experimental results. The results presented in this study can provide references to the design of the moonpool of a drillship.

Experimental and numerical investigations of hydrodynamic response of biodegradable drifting Fish Aggregating Devices (FADs) in waves

Fish Aggregating Devices (FADs) are artificial floating objects deployed in tropical and subtropical pelagic oceans to attract tuna species for capture. Understanding the wave-induced drifting behavior can optimize the dynamical stability of drifting FADs in oceans and improve catchability. In this study, to investigate the dominant factors for stable performance and the validity of different drifting FADs the model experiments of hydrodynamic responses of 14 types of biodegradable drifting FADs models in heave motion and pitch motion are carried out in regular wave conditions. Numerical simulations of three of the models are implemented, and the experimental results are used to validate the results of the numerical simulations. In the numerical simulation, Reynolds-averaged Navier-Stokes (RANS) solver, a realizable k-ε model with two-layer, all y + wall treatment and wave forcing method based on the Euler Overlay Method (EOM) for wave generating and wave absorbing are performed. The results show that the numerical results agreed well with the experimental values. The effects of wave steepness, relative length, relative width, cover object, hanging object, and weight of sinker on the FADs are analyzed. The results indicate that with the constant wave amplitude, the heave motion response increases significantly as the wave period increase, and opposed to the pitch motion response. Wave steepness, relative length, relative width, and the length of the FADs model have an important influence on the motion response amplitude operators (RAO) of the FADs. The FADs model constructed with netting panel and rope as cover object and hanging object, and weighted by a 2.00 kg sinker behaved the most stable behavior among all the models. This study can be used to find out the interaction between waves and the FADs and provide guidance on the design of high-performance biodegradable FADs with stabilization and a long lifespan in harsh pelagic ocean environments.

FULL-SCALE MOTIONS OF A LARGE HIGH-SPEED CATAMARAN: THE INFLUENCE OF WAVE ENVIRONMENT, SPEED AND RIDE CONTROL SYSTEM

To assess the behaviour of large high-speed catamarans in severe seas, extensive full-scale trials were conducted by the U.S. Navy on an INCAT Tasmania built vessel in the North Sea and North Atlantic region. Systematic testing was done for different speeds, sea states and ride control settings at different headings. Collected data has been used to characterise the ship’s motions and seakeeping performance with respect to wave environment, vessel speed and ride control system. Motion response amplitude operators were derived and compared with results from a two-dimensional Green function time-domain strip theory seakeeping prediction method. An increase of motion response with increasing vessel speed and a decrease with the vessel moving from head to beam seas was found. In higher sea states and headings ahead of beam seas an increasing influence of the centre bow on pitch motion damping was found. Significant motion RAO reduction was also found when the ride control system was active. Its effectiveness increased at higher speeds and contributed to heave and pitch motion RAO reduction. Predicted motion magnitudes with the time domain seakeeping code were consistent with the measured motion responses, but maximum heave was predicted at a rather higher frequency than was evident in the trials.

Experimental study of the state-of-the-art offshore system integrating a floating offshore wind turbine with a steel fish farming cage

An innovative offshore system integrating a floating offshore wind turbine with a steel fish farming cage (FOWT-SFFC) has recently been developed by the two leading authors for offshore wind and aquaculture industry. The purpose of this paper is to investigate the dynamic responses of FOWT-SFFC subjected to simultaneous wind and wave actions in the harsh South China Sea environment by a series of model tests. The tests are conducted at the Tsinghua Ocean Engineering Basin with Froude scale of 1:30. In this paper, the similarity law and setup of model tests are given first. Then a series of calibration tests and identification tests are carried out to validate the capacity of wind generator and wave maker, and to identify the vibration frequencies of tower, the stiffness of mooring system, natural periods and system damping, motion response amplitude operators (RAOs) of FOWT-SFFC, and thrust-speed performance of the turbine in wave basin. After that, seakeeping tests are implemented for random waves, followed by a sequence of load cases including normal operating and extreme conditions. Constant wind speeds and random wind speeds are respectively considered in load combinations. The experimental results affirm the excellent seakeeping and dynamic performance of FOWT-SFFC. Existence of metal fish nets increases the damping of foundation's 6 degree-of-freedoms motions. Generally, the influence of nets on the dynamic responses is insignificant in wind sea states.

Round Robin Laboratory Testing of a Scaled 10 MW Floating Horizontal Axis Wind Turbine

This paper documents the round robin testing campaign carried out on a floating wind turbine as part of the EU H2020 MaRINET2 project. A 1/60th scale model of a 10 MW floating platform was tested in wave basins in four different locations around Europe. The tests carried out in each facility included decay tests, tests in regular and irregular waves with and without wind thrust, and tests to characterise the mooring system as well as the model itself. For the tests in wind, only the thrust of the turbine was considered and it was fixed to pre-selected levels. Hence, this work focuses on the hydrodynamic responses of a semi-submersible floating foundation. It was found that the global surge stiffness was comparable across facilities, except in one case where different azimuth angles were used for the mooring lines. Heave and pitch had the same stiffness coefficient and periods for all basins. Response Amplitude Operators (RAOs) were used to compare the responses in waves from all facilities. The shape of the motion RAOs were globally similar for all basins except around some particular frequencies. As the results were non-linear around the resonance and cancellation frequencies, the differences between facilities were magnified at these frequencies. Surge motions were significantly impacted by reflections leading to large differences in these RAOs between all basins.

Numerical and Experimental Analyses on Motion Responses on Heaving Point Absorbers Connected to Large Semi-Submersibles

This study considers the motion responses of heaving point absorbers (HPAs) connected to large semi-submersibles. To analyze the motion responses for HPAs, a motion response amplitude operator (RAO) of a single HPA connected to a fixed wall was obtained in a two-dimensional wave flume. A frequency-domain eigenvalue analysis is used to evaluate the motion RAO of a single HPA, and the experimental and numerical results of motion RAO were compared. A model test was conducted to analyze the motions of multiple HPAs connected to a large semi-submersible in a 3D ocean basin. The motion RAOs of the multiple HPAs connected to the large semi-submersible were compared with the motion RAO of the single HPA connected to the fixed wall.

Design and comparative analysis of alternative mooring systems for floating wind turbines in shallow water with emphasis on ultimate limit state design

Floating wind turbines represent a cost-efficient energy solution in deep water where bottom-fixed wind turbine becomes excessively expensive. However, mooring design is quite challenging for all shallow water depths including the transition water depth between bottom-fixed and floating wind turbines, in the order of 50–80 m, for which floating concepts might become more cost-effective than bottom-fixed ones. In this paper, mooring system design for floating wind turbine in shallow water are studied considering both catenary and taut mooring systems. Seven mooring concepts designed for a 5 MW semi-submersible floating wind turbine at 50 m water depth are compared with the purpose to identify solutions that are structurally reliable and economically attractive. The concepts are made of different mooring line materials (chain and synthetic fibre rope), mooring components (clump weight and buoy) and anchors (drag embedment anchor and suction anchor). Based on the latest experimental data, the nonlinear tension-dependent stiffness of synthetic fibre rope are described with an improved numerical model. Performance of the seven mooring concepts are compared with respect to mooring line characteristics, motion response amplitude operator, utilization factor considering the ultimate limit state design and cost etc. Six mooring design concepts are finally recommended for future assessment regarding the application of floating wind turbines in shallow water say 50 m and deeper.

Study of a deep draft vessel to enhance onsite installation capability of a jack up type unit operating in the wind farm zone offshore of the Taichung Harbor Taiwan

In the paper, a concept of placing a deep draft vessel upstream a jack up type unit is proposed to enhance onsite installation capability of the jack up type unit operating in the wind farm zone offshore of the Taichung Harbor Taiwan, where water depth is less 50m and bottom fixed structures are used. The deep draft vessel intends to induce wave shielding effect to reduce the motions of the downstream jack up type unit during the initial phase of its onsite installation, while its legs/spudcans are not yet touching the seabed and it is still in free floating condition. In general, the more the motion of the jack up type unit is reduced during the initial phase of its onsite installation, the more its onsite installation capability is enhanced. ANSYS AQWA is utilized to analyze the motions of the two floating bodies, the deep draft vessel and the jack up type unit, as well as the wave shielding effect for various wave periods and incident angles. In the analysis, fluid is assumed ideal, and no viscous effect is considered in the calculation of all the motions of the two floating bodies. Pitch and heave motion RAOs (Response Amplitude Operator) of the jack up unit with or without the deep draft vessel placing upstream are compared to examine the wave shielding effect. In the study, a parametric study for a range variation of the principal dimensions of the two floating bodies is performed to determine suitable principal dimensions for the deep draft vessel and the feasibility of the proposed concept. In addition, pitch and heave motion RAOs of the deep draft vessel at wave incident angles of 0°~30° are also analyzed to evaluate its seakeeping performance. From the results of the study, it is found that the vessel with deeper draft (≥12.5 m) is more effective to induce wave shielding effect in waves with period of 5–7 s. The deeper the draft of the vessel, the greater the wave shielding effect, and the more motion reduction to the downstream jack up type unit in waves with period of 5–7 s. It is also found that, in waves with period of 5–7 s and at incident angles of 0°~30°, the vessel with deeper draft has better seakeeping performance. Since the most common waves in the wind farm zone offshore of the Taichung Harbor Taiwan are of 6–7 s in period, the feasibility of the concept of placing a deep draft vessel upstream a jack up type unit to reduce the motion and enhance the onsite installation capability of the jack up type unit operating in that area is demonstrated.

Effects of Fish Nets on the Nonlinear Dynamic Performance of a Floating Offshore Wind Turbine Integrated with a Steel Fish Farming Cage

This paper aims to study the effects of fish nets on the nonlinear dynamic performance of a floating offshore wind turbine integrated with a steel fish farming cage (FOWT-SFFC). Fully coupled aero-hydro-servo-elastic numerical models of FOWT-SFFC, with and without nets, are constructed to probe the nonlinear time-domain stochastic response. The first-order potential flow model with quadratic drag forces is employed to calculate the hydrodynamic loading on the foundation. The effects of nets on the damping ratios of 6 degree-of-freedom motions and on their displacement response amplitude operators (RAOs) are respectively investigated in numerical decay tests and monochromatic regular waves. The results show that the nets help to increase the damping level for the whole system and reduce motion RAOs when wave periods are around the natural periods of motions, while nets play insignificant role in motions when wave periods are far away from motion natural periods. The dynamic performances of FOWT-SFFC with and without nets under random ocean waves, the combined random wind and random waves as well as current are comprehensively compared and discussed. The simulation results indicate that in wind-sea dominated conditions, the nets tend to slightly increase the dynamic responses of FOWT-SFFC, especially the components corresponding to natural periods. Nonetheless, under sea states that comprise both wind-sea waves and swell, nets help to reduce the dynamic responses of FOWT-SFFC by introducing additional damping.

Numerical and Experimental Investigation of Hydrodynamic Interactions of Two VLFS Modules Deployed in Tandem

This paper numerically and experimentally investigates the hydrodynamic interaction between two semi-submersible type VLFS modules in the frequency domain. Model tests were conducted to investigate the relationship between interactions and wave headings. Numerical studies were performed by solving the radiation-diffraction problem and were validated against the experimental results. Motion Response Amplitude Operators (RAOs) were obtained from numerical and experimental studies. The dependency of the hydrodynamic interaction effect on wave headings is clarified. The influence of different wave periods on the motion responses of two-module VLFS and wave elevations in the gap is studied. The results indicate that the hydrodynamic interactions of the two modules are directly related to the wave headings and the periods of the incident wave. The shielding effect plays an important role in short wave, and the influence decreases with the increase of the incident wavelength. The numerical results based on the diffraction-radiation code can give a relatively good estimation to the responses in short wave while for long wave, it would over-predict the response.

An Offshore Floating Wind–Solar–Aquaculture System: Concept Design and Extreme Response in Survival Conditions

This study presents a new concept design combining multiple megawatt (MW) vertical-axis wind turbines (VAWTs) and a solar array with a floating steel fish-farming cage. This combined wind–solar–aquaculture (WSA) system is intended to utilize the ocean space and water resources more effectively and more economically, while greatly shortening the payback period of investment in offshore power generation. The details of this WSA design are described, showing that a square-shaped fishing cage serves as a floating foundation for the 7600 m2 solar array and four multi MW VAWTs. The WAMIT program based on potential-flow theory is employed to obtain the WSA’s motion response amplitude operators (RAOs) in sinusoidal waves of varying periods. The motion RAOs indicated that the proposed concept possesses better hydrodynamic seakeeping performances than its OC3Hywind spar and OC4DeepCwind semi-submersible counterparts. A potential site located in the northwest South China Sea is selected to deploy the WSA. Its feasibility is then examined in terms of the hydrodynamic motions and structural dynamic response driven by wind, waves, and current. Fully coupled time-domain simulations are carried out for 50-year survival conditions. The whole structure exhibits outstanding performance for its small motions in random wind and seas. Moreover, under these survival conditions, the top accelerations and tower base stresses of the VAWTs and mooring line tensions readily meet the design requirements. Technically, the WSA has strong competitiveness and wide prospects in the offshore industry for both power exploitation and marine aquaculture in intermediate and deep waters.

Hydrodynamic-Interaction Analysis of an Autonomous Underwater Hovering Vehicle and Ship with Wave Effects

A new vertical axis-symmetrical dish-shaped autonomous underwater vehicle (AUV) with excellent maneuverability, known as the autonomous underwater hovering vehicle (AUH), is proposed. This study investigates an important working model of the AUH approaching a host ship in waves. The working model of AUH–Ship interactions deals with hydrodynamic interaction, seakeeping performance for communication, launch, and recovery near a free surface. The AUH is able to navigate and implement homing automation through acoustic positioning equipment, a depth sensor, a heading compass, and a Doppler velocity log (DVL) in the working area based on numerical analysis of AUH–Ship hydrodynamic performance in this study. The hydrodynamic-interaction performance of the AUH and ship near free surfaces is analyzed in the frequency and time domains using a potential-based surface-panel method based on a commercial computational fluid dynamics (CFD) solver (ANSYS-AQWA), i.e., a 3D panel code of seakeeping performance module in the ANSYS platform where the fluid is assumed to be irrotational, inviscid, and incompressible. The motion performance of the AUH approaching the host ship, with a dynamic positioning system in waves, is studied by estimating interactive response-amplitude operators (RAOs) of the AUH and host ship in 6-DOF that were estimated and analyzed at different wave amplitudes and frequencies. In the ship and AUH interaction simulations, the host ship is assumed to be a well-posed station keeping in waves with zero service speed. The AUH and ship interference effect is studied at different distances to appropriate recovery and launch positions for the AUH at the following sea and beam sea, i.e., wave-encounter angles 0° and 90°, respectively. In addition, the hydrodynamic interaction of the AUH and ship in yaw and roll at different AUH velocities is estimated. The AUH motion performance approaching the ship in long-crested irregular seas is analyzed in the time domain using the Pierson–Moskowitz wave spectrum model. Viscid hydrodynamic force on AUH motion in roll near a free surface was significant. A damping model was adopted to formulate the viscid effect to enhance the effectiveness of the ANSYS-AQWA inviscid potential-based solver. Numerical analysis of motion RAO of the AUH in roll with the damping effect was compared to the experimental data in wave-frequency range 0.2–1.0 Hz, resulting in the average error being reduced from 21.03% to 9.95% to verify the method’s accuracy. The proposed method conveniently and accurately predicted hydrodynamic-interaction characteristics and motion RAO for a dish-type AUH and host ship for the precise use of mounted sensors in waves. The results of these simulations can be used to analyze the homing automation and adaptive controllability to advance the AUV development and design.

Experimental study on effect of side-mooring lines on dynamics of a catenary moored semi-submersible system

In this article, a novel mooring system with side-mooring lines is proposed for a traditional shape semi-submersible platform with four columns. To obtain the dynamics of moored system, model tests were carried out at a wave basin, including free-decay model tests, white noise model tests and irregular model tests. The natural periods in heave, roll and pitch models were measured and compared with numerical results. The motion response amplitude operators under 90° and 135° waves were obtained from white noise model tests and then compared with numerical simulations. A 100-year sea state in South China Sea was simulated in the wave basin by the JONSWAP spectrum, and the 6-degree-of-freedom motion responses of semi-submersible and mooring tensions were recorded in beam and quartering seas. The effects of the side-mooring lines on the floating platform motion response, mooring tensions and mooring fatigue damage are evaluated by comparing the results with and without side-mooring lines installed.

Numerical research on time domain ship motions coupled with sloshing at different liquid levels and forward speeds

In the present study, an reasonable numerical method based on the potential flow theory and boundary element method (BEM) for solving time domain ship motion coupling with sloshing is proposed. Ship motion is solved based on the three dimensional (3D) time domain potential flow theory with forward speed using the BEM. The 3D fully nonlinear time domain potential flow theory and BEM are also adopted to simulate the nonlinear sloshing phenomenon and then numerically coupled with ship motion in a same time step. A corresponding parallel numerical solver is also developed to investigate the coupling effects between 6 degrees of freedom (DOF) ship motion and internal sloshing. To validate the numerical solver and better understand these coupling effects, numerical research on liquid level and forward speed effects is conducted. The developed numerical solver is also validated from previous model experimental results. Computational and experimental results of ship motion response amplitude operators (RAOs) are in reasonable agreement for both 15000 GT and S175 models with liquid tank. The natural frequency of sloshing varies with changes in liquid levels, and coupling effects become more obvious when the natural frequency of sloshing is close to excited frequency of a ship. Our accurate numerical results on the liquid level effects of roll motions indicate that the numerical method proposed can solve the engineering problem related to liquefied natural gas (LNG) and liquefied petroleum gas (LPG) ships traveling through ocean waves. The numerical behavior of a coupling system with forward speed shows that a liquid tank can reduces the resonance frequency of roll motion and has a limited effect on pitch motion. However, as forward speeds increase, such effects follow a gradually increasing trend.