Parametric Roll Research Articles

A proposed new generation of intact stability criteria for assessment of ship stability in longitudinal waves

Intact ship stability assessment to prevent stability failure in heavy weather conditions is of paramount importance on board vessel. The possibility of assessment the causes that can lead to loss of ship’s stability as well as the assessment of intact stability in heavy seas is a important problem and has attracted a huge interest of the national and international regulatory authorities. Despite the regulations in force, referring to intact ship stability, many ships continued to lose the stability and or capsize due to failure modes that presently are not covered by such regulations. Based on this aspect has been identified the necessity of modelling an updated criteria for assessment of ship’s stability taking into consideration actual possible situations for loss of stability in heavy seas as a measure of increasing she safety of ships. In this respect, the goal of this paper is to illustrate a possible criteria for assessment ship’s stability in heavy seas through a method of determination the possible problems in a form of dynamic stability criteria. A new intact stability criteria is proposed and developed based on separate levels for assessment of vulnerability and susceptibility of ships in situations of parametric rolling and pure loss of stability encountered in extreme sea conditions. Mathematical models correlated with ship’s construction particulars and weather conditions were developed for every separate level in order to assess the ship’s stability. The objective of the proposed criteria is to bring to officers on board ships the possibility of assessment the ship’s intact stability, as a measure of prevention and improvement of safety during the voyage.

A simplified 2½-degree of freedom time-domain model with non-linearity for the simulation of parametric roll

In this paper, a simplified 2½-degree of freedom time-domain numerical method with non-linearity is developed, presented in detail and validated for simulating parametric roll. The method is termed 2½-degree of freedom since; it first linearly couples heave and pitch via a three-dimensional frequency-domain pulsating source method. The roll equation of motion is – then – solved in the time domain with, non-linear damping and non-linear parametric excitation taken into account and formulated in terms of heave-pitch-wave profile influence on roll. In other words, heave and pitch motions influence roll but roll motion does not influence heave and pitch back hence, the term 2½-degree of freedom. The mathematical formulation of the proposed method is presented in detail and has been developed into an in-house numerical model. Subsequently, the numerical model is applied to a modern container ship. Experimental results from the literature are utilized for validation. Predicted results show very good agreement with experiments and demonstrate the ability of the proposed method to accurately capture the influence of various parameters affecting parametric roll.

볼테라 시스템을 이용한 파랑 중 파라메트릭 횡동요에 대한 연구

볼테라 시스템을 이용한 파랑 중 파라메트릭 횡동요에 대한 연구

Model experiments on the early detection and rudder stabilization of KCS parametric roll in head waves

Free running model experiments on the early detection and rudder stabilization of parametric roll in regular and irregular head waves are conducted in the towing tank of Yokohama National University. The KCS (KRISO Container Ship) containership model is used in the experiment. Parametric roll motions are observed in various ship speeds and wave lengths. The parametric roll early detection algorithm based on incremental real-time Hilbert–Huang transform (IR-HHT) technique is validated by the model experiments. Results show that the occurrence of parametric roll under different cases can be successfully detected through the detection algorithm when the roll amplitudes are still small. The rudder anti-roll control is applied for the stabilization of parametric roll in regular and irregular head waves. The rudder anti-rolling is activated when parametric roll is detected by the detection algorithm. It is found that the rudder anti-rolling can successfully stabilize parametric roll in regular and irregular head waves especially when the ship speed is high. However, the effectiveness of rudder anti-rolling is limited in severe parametric roll cases with roll amplitude larger than 25°.

Stochastic analysis of coupled heave-roll ship motion using the domain decomposition chaotic radial basis function

The effect of uncertainties in the roll and heave natural frequencies as well as in the wave amplitude are investigated on the stochastic parametric ship roll motion using the Domain Decomposition Chaotic Radial Basis Function, which is a novel computational scheme proposed here. These uncertain parameters are represented by random variables with arbitrary distribution which in fact constitute the random input of the stochastic model of roll motion. The random input is divided into a number of random subdomains, in which the stochastic heave and the roll motions are represented using the proposed method. By applying the stochastic heave and roll responses in a nonlinear coupled model of heave and roll motions and subsequently employing a Galerkin projection, the deterministic set of equations governing the stochastic parametric roll response in each random domain are obtained. Through presenting various numerical examples, it is shown that the uncertainty in the system and loading parameters can considerably affect the prediction of the statistics of the parametric ship roll response. Further, the numerical results of the method are compared with those of the Monte Carlo simulation method and a very good agreement is obtained while the computational cost is considerably saved.

Comprehensive calculation and safety assessment of parametric roll of very large container ship

As the significant variation of GM in waves for very large container ships, strict demands are raised for this ship type in the evaluation and safety assessment of parametric roll. Targeting a 10 000 TEU container ship sailing in head sea, this study conducts a series of calculations and evaluations on parametric roll motion in which each loading condition is calculated step-by-step. Direct calculation is conducted if neither Level 1 nor Level 2 is satisfied. In this paper, an independently developed time-domain simulation is conducted for loading conditions that fail to match the Level 2 criteria, which is based on a typical 3-DOF weakly nonlinear numerical model. Ship velocity and wave conditions are taken into consideration to explore sensible conditions concerning parametric roll. Finally, according to the results, corresponding safety assessments and several avoidance measures are proposed, such as reducing the height of the center of gravity and raising the speed moderately. In addition, if wave predictions can be detected in advance, the circumstance of the natural rolling period being twice as great as the encountering period should be avoided, which is the most sensible factor for inducing parametric roll. Comprehensive calculation and checking for the 10 000 TEU ship can instruct the general design and improve safety for very large container ships; as a result, remarkable engineering applications and reference value can be recognized.

Towards realistic estimation of ship excessive motions in heavy weather. A case study of a containership in the Pacific Ocean

Synchronous roll and parametric roll resonance are critical phenomena that lead a ship, under certain conditions, to quickly develop large roll amplitudes. This will result in excessive accelerations that can be dangerous for a ship and her cargo. Ships with large bow and stern flare (i.e. container carriers and RoPax) are especially prone to this type of hazards. Therefore, it is of utmost importance for ship operators to be aware of a set of conditions under which these two unwanted phenomena happen. This will help implementing necessary counter measures, either operational (speed or course alterations) or tactical (route finding).In this context, the development of a fast and reliable method for screening the conditions leading to excessive accelerations would improve ship safety. Therefore, in this study, we propose a method detecting critical scenarios for a container ship in heavy weather conditions. The method utilizes an original, six-degree numerical model of ship motions, called LaiDyn, to investigate large amplitude motions and the associated longitudinal and transverse accelerations that a ship is experiencing.Finally, the accelerations that are calculated for a set of operational conditions are checked against their predefined threshold values associated with the cargo lashing system.The proposed method can be used for operational purposes, at the stage of route planning, where the expected accelerations could be considered as another objective function in the route-finding algorithm.

An energy analysis of parametric roll for application to the second generation intact stability criteria

Parametric roll is an amplification of the roll motion due to the periodic variation of the restoring moment in waves. This phenomenon is mostly observed in head and following seas and is the cause of several accidents occurred on container vessels during recent decades. One of the second generation intact stability criteria, currently under finalization and validation by the IMO, requires computing the maximum roll angle with regard to parametric roll. Both proposed methods are relatively complex to implement and require tools that naval architects are not accustomed to. In this paper, we propose an easier alternative method providing the amplitude of parametric roll for any loading condition at any speed, based on energy considerations and assuming a linear GZ. The implementation of this easy method in the corresponding second generation intact stability criterion provides almost the same value of KGmax than the on-degree-of-freedom time simulation proposed by the future regulation.

A Comparative Assessment of Simplified Models for Simulating Parametric Roll

The motion of a ship/offshore platform at sea is governed by a coupled set of nonlinear differential equations. In general, analytical solutions for such systems do not exist and recourse is taken to time-domain simulations to obtain numerical solutions. Each simulation is not only time consuming but also captures only a single realization of the many possible responses. In a design spiral when the concept design of a ship/platform is being iteratively changed, simulating multiple realizations for each interim design is impractical. An analytical approach is preferable as it provides the answer almost instantaneously and does not suffer from the drawback of requiring multiple realizations for statistical confidence. Analytical solutions only exist for simple systems, and hence, there is a need to simplify the nonlinear coupled differential equations into a simplified one degree-of-freedom (DOF) system. While simplified methods make the problem tenable, it is important to check that the system still reflects the dynamics of the complicated system. This paper systematically describes two of the popular simplified parametric roll models in the literature: Volterra GM and improved Grim effective wave (IGEW) roll models. A correction to the existing Volterra GM model described in current literature is proposed to more accurately capture the restoring forces. The simulated roll motion from each model is compared against a corresponding simulation from a nonlinear coupled time-domain simulation tool to check its veracity. Finally, the extent to which each of the models captures the nonlinear phenomenon accurately is discussed in detail.

Boundary Approximations, Effect of Forward Speed and Implementation of Genetic Algorithm in Parametric Rolling

Boundary Approximations, Effect of Forward Speed and Implementation of Genetic Algorithm in Parametric Rolling

Experimental and numerical study of a containership under parametric rolling conditions in waves

A set of scaled model experiments have been conducted at HSVA towing tank to study the occurrence of parametric rolling on a containership in regular and irregular waves. Herein the performed model tests are described and the experimental results are presented. Forced rolling tests were also performed with the ship model in order to investigate its roll damping characteristics. By means of these tests the roll damping coefficients were determined for different maximum roll amplitudes and advance speeds. The experimental data of this containership is compared with results from a non-linear time domain model, where the prediction of maximum roll amplitude under parametric rolling conditions associated with different viscous roll damping models is thoroughly discussed.

KGmax curves associated with second generation intact stability criteria for different types of ships

Currently, second generation intact stability criteria are being developed and evaluated by the International Maritime Organization (IMO). In this paper, we briefly present levels 1 and 2 assessment methods for the criteria of pure loss of stability and parametric roll failure modes. Subsequently, we show the KGmax curves associated with these criteria. We compute these curves for five different types of ships and compare them with the curves embodied in the current regulations. The results show that the safety margin ensured by the first level-1 method of calculation for both pure loss of stability and parametric roll seems to be excessive in many cases. They also show that the KGmax given by the second level-1 method and by the level-2 method may be very similar. In some cases, the level-2 method can be more conservative than the second level-1 method, which is unanticipated by the future regulation. The KGmax curves associated with parametric roll confirm that the C11 container ship is vulnerable to this failure mode. The computation of the second check coefficient of parametric roll level 2 (C2) for all possible values of KG reveals the existence of both authorized and restricted areas on the surface formed by both the draft and KG, which may replace the classical KGmax curves. In consequence, it is not sufficient to check that C2 is lower than the maximum authorized value (RPR0) for a fixed ship’s loading condition.

A study of hybrid prediction method for ship parametric rolling

The parametric rolling (PR) in the head or following waves has been considered as one of the main stability failure modes in the development of the 2nd generation Intact Stability criterion by the International Maritime Organization (IMO). According to previous studies, the estimation methods of the roll damping affect the prediction of the PR significantly, and most of them are based on experiment data or Ikeda's empirical formula. The accuracy of the estimation method for the roll damping could be a key aspect for the validity of its prediction for the full scale ship. In this research, a hybrid prediction method is developed for the numerical prediction of the parametric rolling when experiment data are not available for the roll damping. Comparison study is also carried out between the hybrid method and a nonlinear dynamics method, where the roll damping is estimated by the simplified Ikeda's method and the direct CFD prediction method in a direct non-linear simulation based on the 3-D CFD approach in the model scale. It is shown that the results of the hybrid method are in satisfactory agreements with the model experiment results, and the method can be used for analysis especially at the early design stage where experiment data are often not available.

Efficient Monte Carlo simulation and Grim effective wave model for predicting the extreme response of a vessel rolling in random head seas

In this paper, a computationally efficient Monte Carlo simulation (MCS) approach is introduced in order to estimate the extreme response statistics of parametric rolling in random longitudinal seas. Basically, parametric roll is caused by sufficiently large oscillations of the roll restoring moment occurring within certain frequencies of wave encounter (approximately twice the natural roll frequency). The concept of the Grim effective wave is applied herein in order to approximate the variation of the restoring moment in random waves. A fourth order linear filter is introduced to model the random effective wave amplitude process, which is assumed to be the driving process for the variation of the restoring term as well as for the stochastic nonlinear system of the roll motion by application of the Grim effective wave approximation. For the stochastic dynamical system, the roll response is a random process and an extrapolation procedure is developed for estimating the extreme values of the response statistics by assuming regular behavior in the tail region of the mean upcrossing rate. The rationality of the linear filter model and the feasibility of an efficient MCS method based on extrapolation techniques for predicting the extreme roll response are illustrated. Furthermore, the phenomenon of parametric roll in random seas as well as the effect of vessel speed on the stochastic roll response are investigated.

Application of fin system to reduce pitch motion

Container ships are prone to move at a greater speed compared to other merchant ships. The slenderness of the hull of container vessel is for better speed, but it leads to unfavorable motions. The pitch and roll are related and sometimes the vessel might be forced to parametric roll condition which is very dangerous. A fin attached to the ship hull proves to be more efficient in controlling the pitch. The fin is fitted at a lowest possible location of the hull surface and it is at the bow part of the ship. Simulations are done using proven software package ANSYS AQWA and the results are compared. Simulations are done for both regular and irregular seas and the effect of fin on ship motion is studied. P-M spectrum is considered for various sea states.

A study on the effect of parametric roll on added resistance in regular head seas

Both parametric roll and added resistance in head seas are hot topics in ship hydrodynamics. Parametric roll with half the encounter frequency is usually not taken into account in the calculation of added resistance in regular head seas. In order to study the correlation between parametric roll and added resistance, firstly, a formula of added resistance in regular head seas with parametric roll taken into account based on Maruo theory is developed to investigate the effect of parametric roll on added resistance in regular head seas. Secondly, partially restrained free running experiments with and without roll motions are carried out respectively to investigate the effects of parametric roll on added resistance in regular head seas. The results of experiments and simulations using the C11 containership show that added resistance is affected by parametric roll, and the results of experiments also show that heave and pitch motions are distinctly affected by parametric roll.

Experimental and numerical study on several crucial elements for predicting parametric roll in regular head seas

The methods for direct stability assessment of parametric roll are currently under development at the International Maritime Organization for the second generation intact stability criteria. To establish guidelines for developing accurate, but sufficiently simple prediction method, several elements required for modeling parametric roll in head waves are investigated by executing free running model experiments, partially restrained model experiments with and without surge motion and numerical simulations of uncoupled roll model, coupled surge–roll model and coupled heave–pitch–roll model for a C11 class containership. As a result, the following outcomes are obtained. First, the surge effect on parametric roll is generally small. Second, heave and pitch motions can have subharmonic components when parametric roll occurs. Third, the inclusion of the radiation and diffraction effects on restoring variation can result in more conservative prediction for parametric roll in head seas. Finally, the use of the uncoupled roll model could provide more conservative, but less time-consuming prediction for parametric roll than that of coupled heave–pitch–roll model.

Numerical prediction of parametric roll in oblique waves

Numerical prediction of parametric roll in head and following waves has been intensively investigated so that the requirements for a reasonably good prediction are almost entirely known. However, prediction of parametric roll in oblique waves has not yet been sufficiently investigated owing to the unavoidable coupling with sway and yaw motions. Since parametric roll for actual ships occurs with almost zero forward velocity, accurate prediction of the sideways drift of the ship in waves is difficult. Therefore, in this study, the authors present a numerical model of parametric roll in oblique waves by considering low-speed manoeuvring forces. The numerical predictions are compared with newly performed free-running model experiments of a hypothetical ship, in which the maximum roll amplitude was about 20°. The obtained results show that the present model captures some qualitative tendencies in the experiment but the estimated amplitudes are larger than the experiment by about 7°. This information can be used to identify the minimum requirements for good prediction of parametric roll in oblique waves.

URANS simulations for a flooded ship in calm water and regular beam waves

CFD simulations are conducted for zero-speed damaged passenger ship SSRC in calm water and waves with 6DOF motions including flooding procedure in calm water, roll decay in calm water and motions in regular beam waves for various wavelengths. The simulations model the 6DOF soft spring experimental mount, the one- and two-room flooding compartment configurations, including both intact and damaged conditions. For flooding and roll decay, simulations show ability to predict the trend of increases in roll period and damping due to flooding, as reported in ITTC. The damping magnitudes were often under-predicted with large errors while the roll period and compartment water height were well predicted. Two-room compartment simulation showed three times larger damping than one-room compartment cases whereas the roll period was similar for both conditions. For wave cases, all motions show primarily 1st order responses, except for parametric roll condition which shows large ½ harmonic responses for the intact ship. The 2nd order responses are small for both damaged and intact ship. The larger roll period and damping for the damaged ship shift the peak of responses to smaller wave frequency and reduce the amplitude of responses. The average error is often large for 1st order intact ship pitch and damaged ship surge and pitch. The errors are larger for most ½ and 2nd order responses. Large errors could be partially due to the complex mounting system in the experiment. Overall, current CFD results show better predictions than those reported for potential flow solvers even though the computational cost is larger.

VISIR-I: small vessels – least-time nautical routes using wave forecasts

Abstract. A new numerical model for the on-demand computation of optimal ship routes based on sea-state forecasts has been developed. The model, named VISIR (discoVerIng Safe and effIcient Routes) is designed to support decision-makers when planning a marine voyage. The first version of the system, VISIR-I, considers medium and small motor vessels with lengths of up to a few tens of metres and a displacement hull. The model is comprised of three components: a route optimization algorithm, a mechanical model of the ship, and a processor of the environmental fields. The optimization algorithm is based on a graph-search method with time-dependent edge weights. The algorithm is also able to compute a voluntary ship speed reduction. The ship model accounts for calm water and added wave resistance by making use of just the principal particulars of the vessel as input parameters. It also checks the optimal route for parametric roll, pure loss of stability, and surfriding/broaching-to hazard conditions. The processor of the environmental fields employs significant wave height, wave spectrum peak period, and wave direction forecast fields as input. The topological issues of coastal navigation (islands, peninsulas, narrow passages) are addressed. Examples of VISIR-I routes in the Mediterranean Sea are provided. The optimal route may be longer in terms of miles sailed and yet it is faster and safer than the geodetic route between the same departure and arrival locations. Time savings up to 2.7 % and route lengthening up to 3.2 % are found for the case studies analysed. However, there is no upper bound for the magnitude of the changes of such route metrics, which especially in case of extreme sea states can be much greater. Route diversions result from the safety constraints and the fact that the algorithm takes into account the full temporal evolution and spatial variability of the environmental fields.