Stern Quartering Waves Research Articles

Further Study on One of the Numerical Methods for Pure Loss of Stability in Stern Quartering Waves

The International Maritime Organization (IMO) finalized the second-generation intact stability criteria in 2022. However, an accurate and practical numerical method for stability loss has yet to be established. Therefore, a 6 DOF numerical model is further improved based on the previous study. Firstly, the rolling motion is simulated using a seakeeping model instead of the previous maneuvering mathematical model. Secondly, the roll-restoring variation is calculated directly considering the instantaneous wet hull instead of the previous pre-calculated method. Thirdly, transferring frequency to time is used to obtain heave and pitch motions, further considering yaw angle and sway velocity. Fourthly, the dynamic forces for sway, roll, and yaw motions are calculated, further considering the effect of the speed variation. Fifthly, the 6 DOF motions are used to determine the instantaneous wet hull, and the FK force and the hydrostatic force are calculated by the body’s exact method. Finally, a new conclusion is obtained that the sway and yaw motions’ effect on the ship speed loss, the relative longitudinal wave profile by the speed loss, the rudder angles, and the accompanying rudder forces in the rolling direction are significant, and much more than their centrifugal force or coupled force in the rolling direction.

Probabilistic estimation of the large heel due to broaching associated with surf-riding for a ship in short-crested irregular waves and its experimental validation

The International Maritime Organization started using a numerical simulation to quantify the probability of a ship's stability failure as a direct stability assessment for broaching associated with surf-riding. Some of the authors proposed a critical wave method to estimate such probability, and its numerical verification and experimental validation in long-crested irregular stern-quartering waves were already published. The remaining issue is numerically verifying and experimentally validating the methodology applied to short-crested irregular stern-quartering waves. The work described in this paper is an attempt to resolve this remaining issue by executing numerical simulation and a free-running model experiment in both short-crested and long-crested irregular waves. The subject ship used in this work is an ocean research ship similar to the one lost in actual stern-quartering waves with higher speed, which was used in our previous study in regular waves. The experimental results indicate that the direct counting in the numerical simulation shows stochastically sufficient agreement with the model experiment, and the critical wave method provides reasonably conservative estimates even in short-crested irregular waves.

On the use of dynamic mode decomposition for time-series forecasting of ships operating in waves

In order to guarantee the safety of payload, crew, and structures, ships must exhibit good seakeeping, maneuverability, and structural-response performance, also when they operate in adverse weather conditions. In this context, the availability of forecasting methods to be included within model-predictive control approaches may represent a decisive factor. Here, a data-driven and equation-free modeling approach for forecasting of trajectories, motions, and forces of ships in waves is presented, based on dynamic mode decomposition (DMD). DMD is a data-driven modeling method, which provides a linear finite-dimensional representation of a possibly nonlinear system dynamics by means of a set of modes with associated frequencies. Its use for ship operating in waves has been little discussed and a systematic analysis of its forecasting capabilities is still needed in this context. Here, a statistical analysis of DMD forecasting capabilities is presented for ships in waves, including standard and augmented DMD. The statistical assessment uses multiple time series, studying the effects of the number of input/output waves, time steps, time derivatives, along with the use of time-shifted copies of time series by the Hankel matrix. The assessment of the forecasting capabilities is based on four metrics: normalized root mean square error, Pearson correlation coefficient, average angle measure, and normalized average minimum/maximum absolute error. Two test cases are used for the assessment: the course keeping of a self-propelled 5415M in irregular stern-quartering waves and the turning-circle of a free-running self-propelled KRISO Container Ship in regular waves. Results are overall promising and show how state augmentation (using from four to eight input waves, up to two time derivatives, and four time-shifted copies) improves the DMD forecasting capabilities up to two wave encounter periods in the future. Furthermore, DMD provides a method to identify the most important modes, shedding some light onto the physics of the underlying system dynamics.

Time-series forecasting of ships maneuvering in waves via dynamic mode decomposition

A data-driven and equation-free approach is proposed and discussed to forecast responses of ships maneuvering in waves, based on the dynamic mode decomposition (DMD). DMD is a dimensionality-reduction/reduced-order modeling method, which provides a linear finite-dimensional representation of a possibly nonlinear system dynamics by means of a set of modes with associated oscillation frequencies and decay/growth rates. This linear representation is entirely derived from available data and does not require the knowledge of the underlying system equations, which are and remain unknown. Based on the linear representation, DMD allows for short-term future estimates of the system state, which can be used for real-time prediction and control. Here, the objective of the DMD is the analysis and forecast of the trajectories/motions/forces of ships operating in waves, offering a complementary efficient method to equation-based system identification approaches. Results are presented for the course keeping of a free-running naval destroyer (5415M) in irregular stern-quartering waves and for the free-running KRISO Container Ship performing a turning circle in regular waves. Results are overall promising and show how DMD is able to identify the most important modes and forecast the system state with reasonable accuracy upto two wave encounter periods.

Study on extreme roll event with capsizing induced by pure loss of stability for the free-running ONR Tumblehome

International Maritime Organization (IMO) has stated that the direct assessment for the pure loss of stability, one of the typical stability failure modes, is necessary for ship designers and under development currently. In this study, extreme roll motions with large amplitudes, induced by the pure loss of stability, are predicted for a benchmark combatant ONR Tumblehome running in stern quartering waves by the computational fluid dynamics (CFD) simulations. An unsteady Reynolds-averaged Navier–Stokes (RANS) solver coupled with a dynamic overset grid approach is used to predict six degree of freedom (DOF) motions. The discretized propeller model is applied to the free-running model, along with a course keeping controller. Different speed conditions are considered for the ship to investigate the instability zone where the pure loss of stability occurs and the CFD results for the roll amplitude are compared with the experimental data, with an average difference less than 3%. In addition, it is observed that ship capsizing occurs coupled with a rapid increase of yaw angle, which is consistent with the phenomenon in the existed model tests. Overall, it indicates that this viscous simulation model is capable for the prediction of the extreme roll as well as the capsizing.

Experimental study on turning characteristics of KVLCC2 tanker in long-crested irregular waves

In this paper, turning characteristics of KVLCC2 tanker in long-crested irregular waves are investigated by 1/100 scaled free-running model tests. Three kinds of model propulsion points are determined in calm water tests, which correspond to the full-scale calm water speeds of 4.0, 7.0, and 15.5 knots. Turning circle tests are performed in long-crested irregular head waves of sea state 5 and 6, with variations of the model propulsion points. In order to obtain the statistical data on the manoeuvring behaviours of the model in irregular waves, irregular waves per each sea state are generated with five seeds, in other words, five kinds of superposition of regular waves. Initial and steady turning characteristics of the model ship are analyzed by using the indices proposed in the previous studies. The deviations of initial turn trajectories depending on sea state are relatively small, compared to the deviations of steady turn trajectories. Drifting distances of steady turns increase with increasing sea states, and they are remarkably increased with decreasing ship advance speeds. With the lowest model propulsion point corresponding to full-scale 4 knots, the model ship cannot turn in most runs under sea state 6 waves. Next, with the model propulsion point corresponding to full-scale speed of 7 knots, turning circle tests are performed in regular waves in order to compare the trajectory drifts in regular waves with those in irregular waves. Five kinds of regular waves are generated following the representative parameters of sea state 6 irregular waves such as significant, mean heights, modal, mean, and energy periods. Turning trajectories in regular waves are most similar to those in irregular waves in case that the regular waves have the mean height and the energy period of irregular waves. Finally, course-keeping and +35° initial turning tests with lowest propulsion point are carried out in sea state 6 long-crested irregular waves, in order to investigate low speed course-keeping and turning abilities depending on the wave incident angles. Wave incident angles are varied from 30° to 330° at intervals of 30°. In port beam and port stern quartering waves, the steering moments by rudder cannot overcome the wave drifting forces and moments, so the model ship has problems on course-keeping and turning manoeuvres.

URANS analysis of a free-running destroyer sailing in irregular stern-quartering waves at sea state 7

Computational fluid dynamics (CFD) simulations and stochastic validation of free-running 5415M in irregular stern-quartering sea state 7 and Froude number 0.33 are presented. Unsteady Reynolds-averaged Navier–Stokes (URANS) computations are validated against experimental fluid dynamics (EFD) tests. EFD static stability, forward speed, wave direction and spectrum were set such that roll-motion resonance were induced, causing large roll angles, significant deck-edge immersion, and static instability. Prerequisite calm-water validation covers roll decay at zero speed and self-propulsion studies for propeller RPM. Subsequent CFD stochastic validation is achieved by statistical assessment of EFD data and CFD results (expected value, standard deviation, and probability distribution) for input waves and ship response: time series are assessed by their wave energy-spectra, autocovariance (waves only), and block-bootstrap analysis (waves and motions); mean-crossing amplitudes are studied by bootstrap method. Dynamic mode decomposition is used with EFD and CFD time histories to unveil the underlying ship dynamics and the motion correlation. Overall, CFD results are in agreement with EFD. Finally, a clustering approach is used to identify wave sequences causing large roll angles. As proof of concept, the characteristics of these sequences are used for the deterministic reconstruction of severe (large roll) and rare (capsize) events via regular wave computations.

Effect of separation vortices on wave-induced sway force and yaw moment acting on a ship running in stern quartering waves

Effect of separation vortices on wave-induced sway force and yaw moment acting on a ship running in stern quartering waves

Model experiments and direct stability assessments on pure loss of stability in stern quartering waves

The criteria for direct stability assessment of pure loss of stability are currently under development at IMO as part of second-generation intact stability criteria. For providing an accurate and practical mathematical model, a four-stage approach has been adopted herein. Firstly, a surge-sway-heave-roll-pitch-yaw coupled mathematical model (6-DOF) is newly established, with unified expressions based on an MMG standard method and existing mathematical models of broaching and parametric rolling. The heave and pitch motions are obtained by a strip method with the speed variation considered. They determine the instantaneous relative position of the ship to waves. Then, the corresponding nonlinear Froude-Krylov roll restoring variation is calculated by integrating the wave pressure up to the wave surface. Secondly, model tests are carried out in stern quartering waves to validate the predictions. Thereafter, the effect of some crucial terms on the prediction is studied. Terms such as the higher-order manoeuvring coefficients, the rudder force, the diffraction forces are investigated. Finally, the types of roll motions observed during pure loss of stability are identified. The results show that pure loss of stability is not “pure” but the proposed coupled 6-DOF model can be utilized for the direct assessment of the vulnerability at this failure mode.

Effectiveness and mechanism of broaching-to prevention using global optimal control with evolution strategy (CMA-ES)

This paper demonstrates the effectiveness of using global optimal rudder control with the covariance matrix adaptation evolution strategy, applied to a surge-sway-yaw-roll coupled numerical model, in preventing broaching-to, occurring under conventional PD rudder controls in stern quartering waves. In particular, the PD control with optimized PD parameters is more efficient than the time history-optimized approach. With the help of stability analysis of surf-riding equilibria, two different mechanisms to successfully prevent broaching-to were identified: one is to tend to a periodic orbit with additional slight rudder actions and the other is to stay in surf-riding on a position of unstable equilibrium in regular waves for a longer duration with a larger differential gain. These outcomes could facilitate real-time prevention of broaching-to in actual seas.

Water-on-deck effects on roll motions of an offshore supply vessel in regular stern quartering waves

The applicability of the second generation intact stability criteria for preventing pure loss of stability in astern waves to offshore supply vessels (OSV) is investigated. OSVs show an inconsistency problem in the first and second level criteria. Thus, free-running model experiments of an OSV by changing its length of low weather deck in regular stern quartering waves were conducted and were compared with numerical simulation used for pure loss of stability so far. As a result, it was confirmed that the effects of water on deck (WOD) on the behaviour of the OSV could prevent the occurrence of typical pure loss of stability for the cases of long low weather deck. One of WOD's effects is the increase of roll damping and the other is the loss of static stability.

ONR Tumblehome course keeping and maneuvering in calm water and waves

This paper discusses the maneuvering performance of the Office of Naval Research Tumblehome (ONRT) surface combatant model in waves. Maneuvering tests in calm water and regular waves using free-running model were conducted at the IIHR wave basin, The University of Iowa. Ship trajectories and 6DOF motions/velocities were obtained for all tests. Course keeping tests were performed in 8 variable headings for three wave lengths and harmonic analysis were done for measured variables. The 1st harmonic amplitude of pitch and heave have maximum value in head waves and beam waves, respectively. Other amplitudes except for these two have maximum value at stern quartering waves. Zigzag and turning tests were performed in calm water and in waves. Maneuvering characteristic parameters such as 1st and 2nd overshoot angles, advance and tactical diameter in calm water were evaluated based on the International Maritime Organization (IMO) criteria. Maneuvering characteristic parameter of zigzag and turning in waves were also evaluated and compared to those of S-175 and Very Large Crude Carrier (VLCC). It is confirmed that ONRT satisfies IMO criteria and has higher maneuverability than S-175 and VLCC due to its slender hull with the twin-rudder twin-screw.

Multidisciplinary experiment using steep regular waves to determine ship operating conditions that avoid capsize

This paper explores using steep regular waves to identifying safe operating conditions that avoid capsize. The data is from a multidisciplinary experiment using an autonomous scale-model running a proportional-derivative controller in aft of beam steep regular waves. The test explored relative wave headings from 15 $$^\circ $$ to 75 $$^\circ $$ and speeds from 0.1 to 0.4 Froude number. This effort analyzes the resultant ship trajectories to determine if the model obtained the desired operating conditions during each run. For slow speeds, safe operating conditions could not be identified since the requested headings could not be achieved. For moderate speeds, most requested headings could be achieved. At the highest speeds, only relative wave headings closer to beam seas could be explored as the model capsized in stern quartering waves. Results show that wavelength and wave steepness have minimal effects on the model’s ability to achieve a desired heading. Finally, only a limited number of runs are required to verify a safe operating condition since capsizes appear to be consistently repeatable. This research highlights the usefulness of using steep regular waves for capsize testing but also some of its limitations.

Effect of above-waterline hull shape on broaching-induced roll in irregular stern-quartering waves

In this paper, the effect of the above-waterline hull shape on broaching danger in irregular stern-quartering waves was numerically investigated using the US Office of Naval Research (ONR)-tumblehome and ONR-flare hulls. To indicate the danger of broaching, the probability of a broaching-induced large roll angle of the two vessels was examined along with the probability of broaching. The numerically estimated broaching-induced roll angles were compared with the time histories of the free-running model experiments. Then, the effects of above-waterline hull shape on broaching danger in the North Atlantic were simulated for various speeds, autopilot courses and rudder gains.

Broaching probability for a ship in irregular stern-quartering waves: theoretical prediction and experimental validation

To avoid stability failure due to the broaching associated with surf riding, the International Maritime Organization (IMO) has begun to develop multilayered intact stability criteria. A theoretical model using deterministic ship dynamics and stochastic wave theory is a candidate for the highest layer of this scheme. To complete the project, experimental validation of the theoretical method for estimating broaching probability in irregular waves is indispensable. We therefore conducted free-running model experiments using a typical twin-propeller and twin-rudder ship in irregular waves. A simulation model of coupled surge–sway–yaw–roll motion was simultaneously refined. The broaching probability calculated by the theoretical method was within the 95 % confidence interval of that obtained from the experimental data. This could be an example of experimental validation of the theoretical method for estimating the broaching probability when a ship meets a wave.

Calculation of Horizontal Sectional Loads and Torsional Moment

Horizontal sectional loads (horizontal shear force and horizontal bending moment) and torsional moment are more difficult to predict with potential flow methods than vertical loads, especially in stern-quartering waves. Accurate computation of torsional moment is especially important for large modern container ships. The three-dimensional (3D) seakeeping code GL Rankine has been applied previously to the computation of vertical loads in head, following and oblique waves; this paper addresses horizontal loads and torsional moment in oblique waves at various forward speeds for a modern container ship. The results obtained with the Rankine source-patch method are compared with the computations using zero-speed free-surface Green functions and with model experiments.

On the non-linearities of ship's restoring and the Froude-Krylov wave load part

When formulating a general, non-linear mathematical model of ship dynamics in waves the hydrostatic forces and moments along with the Froude-Krylov part of wave load are usually concerned. Normally radiation and the diffraction forces are regarded as linear ones. The paper discusses briefly few approaches, which can be used in this respect. The concerned models attempt to model the non-linearities of the surface waves; both regular and the irregular ones, and the non-linearities of the restoring forces and moments. The approach selected in the Laidyn method, which is meant for the evaluation of large amplitude motions in the 6 degrees-of-freedom, is presented in a bigger detail. The workability of the method is illustrated with the simulation of ship motions in irregular stern quartering waves.

Numerical prediction of the surf-riding threshold of a ship in stern quartering waves in the light of bifurcation theory

In order to develop design and operational criteria to be used at the International Maritime Organization (IMO), critical conditions for broaching are explored in the light of bifurcation analysis. Since surf-riding, which is a prerequisite to broaching, can be regarded as a heteroclinic bifurcation, one of global bifurcations, of a surge-sway-yaw-roll model in quartering waves, the relevant bifurcation condition is formulated with a rigorous mathematical background. Then an efficient numerical solution procedure suitable for tracing the surf-riding threshold hypersurface is presented with successful examples. This deals with all state and control variables in parallel, and excludes backward time integration and an orthogonal condition in the iteration process. The bifurcation conditions identified were compared with the results from a direct numerical simulation in the time domain. As a result, it was confirmed that the heteroclinic bifurcation provides a boundary between motions periodically overtaken by waves and nonperiodic motions such as surf-riding and broaching.

Global wave loads on intact and damaged Ro-Ro ships in regular oblique waves

A nonlinear time-domain simulation method is presented for the prediction of dynamic global wave loads on a Ro-Ro ship at zero speed in regular oblique waves in an intact and a damaged condition. Numerical computations and model tests have been carried to investigate the structural responses of Ro-Ro ship Dextra to various wave amplitudes at three different wave headings (DTR-4.1-NEW-12.98, DEXTREMEL project BE97-4375, 1998; DTR-4.2-NEW-11.99, DEXTREMEL project BE97-4375, 1999). The results of numerical and experimental investigations for stern quartering waves are reviewed. Comparisons between predictions and measurements for global wave loads at the midship section of the intact and the damaged Ro-Ro ship show that the agreement between the theory and experiment for dynamic horizontal and vertical bending moments is excellent. On the other hand, correlation between the predictions and measurements for dynamic vertical shear force is better than that for dynamic horizontal shear force. Nevertheless, the calculated torsion moment values are higher than the measured values. As the wave amplitude is not small, the positive and negative peaks of global wave loads are no longer equal to each other as found in both the calculations and experiments. The dynamic vertical global wave loads in the damaged condition are larger than that in the intact condition.

Large-amplitude motion responses of a Ro-Ro ship to regular oblique waves in intact and damaged conditions

This article presents a nonlinear time-domain simulation method for the prediction of large-amplitude motions of a Ro–Ro ship in regular oblique waves in an intact and a damaged condition. Numerical computations and model tests have been carried out to investigate the dynamic motion responses of Ro–Ro ship Dextra to various wave amplitudes at three different wave headings. The results of numerical and experimental investigations for stern quartering waves are reviewed. Comparisons between predictions and measurements show good agreement except in the roll-resonant region. Nonlinear effects are significant in horizontal modes of motion, and resonant roll motion, and there is strong coupling between all modes of motion in the roll-resonant region for large-amplitude responses. On the other hand, the time-domain simulation technique suffers from numerical drift in horizontal modes of motion as wave amplitude increases. This is due to nonlinear equations of motion and the lack of a restoring force and moment in horizontal motion.