Parametric Roll Research Articles

An insight about roll damping within the second generation intact stability criteria

AbstractDespite the recognized complexity to estimate the damping influence on ship roll motion, some efficient semi-empirical methodologies have been developed along the years to this purpose. CFD methods, in principle the most appropriate tools to predict roll damping, are not a favorite option in preliminary design at present due to their implications in terms of complexity and computational time. In this paper, an integration of the semi-empirical Ikeda’s simplified method has been formulated with modification of the bilge keels and lift components, following a contribution found in the literature and relevant for Ro–Ro ships. Moreover, with focus on damping evaluation, the second generation intact stability criteria (SGISc) have been investigated: the second-level vulnerability criteria for dead ship condition and parametric roll have been applied to a Ro–Ro passenger ship. Both the consolidated and the new proposed roll damping prediction methods have been implemented in order to appreciate their effects on the final outcome.

Research on parametric roll of the polar environmental transport ship based on time-domain Rankine panel method

In this study, the roll damping of a polar environmental transport ship (PETS) is estimated using viscous CFD method, and the parametric roll is simulated based on time-domain Rankine panel method. This method's reliability is validated by contrasting the simulation results with the experimental data of C11 container ship. The roll damping of C11 container ship is estimated using CFD method and improved Ikeda's method, respectively. Then, the time-domain Rankine panel method is adopted to simulate the roll motions of C11 container ship, and the simulation results are contrasted with experimental data. It confirms that the roll damping is calculated by CFD method and the roll motions of ships are simulated based on time-domain Rankine panel method has good applicability. Finally, the influence of wave steepness, wavelength, and the ratio of encounter frequency ωe to natural roll frequency ωroll on the parametric roll of PETS are studied. It is found that the maximum roll angle of PETS increases along with wave steepness. As the wavelength increases, the possibility of parametric roll for PETS is also increasing. When the parametric roll of PETS occurs, the ωe/ωroll tends to increase.

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.

Study on numerical simulation and mitigation of parametric rolling in a container ship under head waves

To investigate the parametric rolling motion of container ships navigating in head seas, this study utilizes the unsteady RANS approach combined with dynamic overlapping grid technology to simulate parametric roll in a container ship under the coupled motions of roll, pitch, and heave. Initially, the model was validated against experimental results, demonstrating good agreement and thus confirming the reliability of the computational method. Furthermore, the paper investigates the impacts of the initial roll angle, encounter frequency, and the addition of bilge keels on parametric rolling. The research findings indicate that the initial angles of rolling impact the duration needed to attain a steady roll condition, yet they have minimal effect on the amplitude post-stabilization. The likelihood of parametric rolling arises when the frequency of encounters doubles that of the ship's inherent roll frequency. Furthermore, the likelihood of parametric rolling escalates when the wavelengths approach the length of the ship. Installing bilge keels markedly reduces the parametric rolling movement in vessels, and the occurrence of parametric rolling is also delayed.

ALGORITHM FOR ESTIMATING THE PARAMETRIC ROLL MOTIONS

For a ship, both synchronous and parametric roll motions can be modelled by nonlinear second-order differential equations with the roll angle as dependent variable and the nonlinearities coming from the damping and restoring moments. In the absence of exact solution techniques, approximate solutions for such equations can be obtained, in principle, analytically or numerically. In this paper, we focused on a fast and accurate recursive scheme based on the segmentation of the time domain into a fine grid of intervals of equal lengths. Due to the smallness of each time subinterval, a reset of the terms of the initial nonlinear equation of motion allows replacing it with a linear one in which the constant coefficients represent approximate values of the former variable coefficients in the middle of each subinterval. The linear equation is solved via the Laplace transform and the resulting solution together with its first derivatives is used to generate the iterative algorithm. This technique was applied to the case of two typical roll equations. The first describes the synchronous roll of a vehicle ferry model equipped or not with bilge keels while the second estimates the parametric roll of a container ship model. In both cases, the analyzed recursive algorithm not only generated results in full agreement with those provided by the ode45 solver in Matlab but also lead to a gain in computation time and offered more flexibility in imposing some restrictive conditions associated, for example, with exceeding some oscillation amplitudes or to the ship capsizing. Key words: synchronous and parametric ship rolling, iterative scheme

The Impact of the new DMS-1030 Stability Standard on the Future Design of Navy Ships

In 2022, the German BAAINBw launched a revised issue of their 1030-1 stability regulations for Navy surface vessels. The improvements of the revised code concerned (inter alia) a new stability criterion for minimizing the effect of parametric rolling combined with pure loss of stability on the wave crest and revised damage stability calculation assumptions, which mainly focus on the submergence of openings and a special treatment of watertight doors. The improvements of the code were found to be necessary to keep track of recent developments in IMO for commercial ships and to update the safety level represented by the code. At the same time, the revised code gives more freedom to the ship designer, a fact which may allow novel and more cost effective concepts of Navy Ships in the near future, provided, the evaluation of the stability according to the code takes place immediately during the very early design phase of the ship. The present paper gives insight into the important updates of the code and it demonstrates at the same time how the design of Navy Ships may benefit from the revised code, if it is applied throughout the very first design phase of the ship. The paper will further present an improved design regime for the early design stage.

Unsteady RANS CFD Simulation on the Parametric Roll of Small Fishing Boat under Different Loading Conditions

Unsteady RANS CFD Simulation on the Parametric Roll of Small Fishing Boat under Different Loading Conditions

Comparison of stochastic stability boundaries for parametrically forced systems with application to ship rolling motion

Numerous accidents caused by parametric rolling have been reported on container ships and pure car carriers (PCCs). Considering this dangerous phenomenon, the parametric rolling in irregular seas is examined in this paper based on the stability of the systems origin, which corresponds to the upright condition of the vessel. It provides a novel theoretical explanation of the instability mechanism for two cases: white-noise parametric excitation and colored-noise parametric excitation. Moreover, the authors confirm the usefulness of the previously provided formulae by Roberts and Dostal by means of numerical examples.

Parametric Roll Motion Reduction of a Ship with a Passive Anti-Roll Tank

In this study, the influence of a U-tube passive anti-roll tank on parametric roll motion has been investigated as a mechanical absorber of a dynamic system. Specifically, this paper concentrates on how the initial conditions of a coupled roll motion and fluid motion in the tank act on the performance of an anti-roll tank. Parametrically excited roll motion was modeled as a single degree of freedom system incorporating heave and pitch effects by means of a time-varying restoring moment. Fluid motion in the tank was modeled as a single degree of freedom system. Coupled equations of motion were solved numerically and the results were presented in the time domain. Furthermore, the results were comparatively depicted as maximum roll amplitudes vs. initial values for a ship with and without an anti-roll U-tube tank.

The effect of a ship's acceleration and deceleration on parametric roll motion in regular head waves at resonance conditions

The effect of a ship's acceleration and deceleration in regular head waves on parametric roll motion is examined experimentally in the study and compared with a mathematical model. Operators queries such as "Should I accelerate or decelerate the ship in resonance condition?" and "Is the magnitude of acceleration or deceleration effective in reducing large roll motion?" are tried to answer. It is well known that waves with lengths similar to that of the ship may suffer parametric roll motion. Additionally, it is possible to say that the encounter frequency itself provides the ship's tuning factor. Since one particular wave is selected with a length equal to the ship's length, the tuning factor in this study at ship operation is the velocity. Results indicate that the amplitudes of roll motion at acceleration and deceleration periods are still large. Results also indicate that the magnitude of acceleration or deceleration affects the roll motion. The mathematical model is also solved numerically and compared with experimental results to better understand the effect of acceleration magnitude.

An Investigation about Stability in Waves of Large Pleasure Yachts

The IMO’s second-generation intact stability criteria (SGISc) have been applied to a set of seven megayacht units ranging from 40 m to 80 m. The application aims to evaluate their stability performance in a seaway. The assessment is based on two vulnerability levels, and the related criteria rely on the physics of the phenomena under investigation (dead ship condition, excessive acceleration, parametric rolling, pure loss of stability, and surf-riding). At the same time, SGISc provide methodological approaches to consider possible operational limitations related to the geographical area the vessel is meant to sail. Results of the comprehensive analysis carried out for the selected megayacht units are presented in term of limiting KG curves. Outcomes pointed out that inconsistencies among vulnerability levels still exist. Further comments about the relation of the investigated vessel typology and relevant operational profile have been reported. In addition, systematic analysis of the effect of the main design parameter on ship rules compliance has been carried out.

Evaluation of Parametric Roll Mode Applying the IMO Second Generation Intact Stability Criteria for 13K Chemical Tanker

In this paper, the evaluation procedure for Level 1, Level 2A, and Level 2B for the parametric roll among the five modes of the IMO second generation stability criteria was explained in detail. Parametric roll mode evaluation was performed using the design data of a medium-sized 13K chemical tanker instead of a well-known container ship. As a result of the Level 1 evaluation, δGM1/GM was smaller than the standard value, thus satisfying the first criterion, but the second criterion value was smaller than 1, so it was found that the Level 1 criterion was not satisfied. Subsequently, in the Level 2A evaluation, the weighted sum value was larger than the standard value under the ship speed and given wave conditions, so it was also not satisfied. In particular, the process of numerical analysis in the time domain was described through the equation of motion when estimating the maximum roll angle of a ship in the Level 2B evaluation, which was not detailed in previous studies. The calculation result was larger than the standard value, so it was not satisfied, and consequently, the 13K chemical tanker did not satisfy Level 1, Level 2A, and 2B.

Research on second level of vulnerability criteria of parametric rolling with stochastic stability theory

The second level of vulnerability criteria of parametric rolling proposed by the International Maritime Organization (IMO) is aimed to evaluate the probability of roll instability and large roll motion of ships in the designated sea areas. Compared with the numerical simulation in random waves, the stability boundary derived from the criteria has large errors. Some additional checks are required in the key region. A new method is proposed to assess ship parametric roll in the designed sea area based on stochastic stability theory. A nonlinear system has the same stability properties as its equivalent linear system. Therefore, the nonlinear parametric rolling motion equation is linearized in order to study its stochastic stability in random waves. Based on the top Lyapunov exponent and the stochastic averaging theory, the expressions for parametric rolling stability boundary are given. The accuracy of these stability boundaries is verified by comparison with numerical simulation. The new method with the stochastic stability boundary can quickly and accurately evaluate the probability of large roll motion of ships in the designated sea areas which illustrates the possibility of improvement to a certain extent.

The improvement of stochastic averaging method to solve the ship rolling response excited by narrow-band waves

The stochastic averaging method of energy envelope can accurately solve the random motion response under the excitation of white noise. The noise had to fulfill the condition of strong mixing which roughly means that the process has to be broad-band. However, the sea conditions in practical engineering conditions are narrow-band spectra. Research on applicability of the stochastic averaging method of energy envelope shows that for narrow-band excitation, the damping of the system and excitation intensity should be small, and the excitation bandwidth should be large. Based on the above background, the improvement of stochastic averaging method of energy envelope under narrow-band waves is studied. The phase angle θ is introduced to characterize the relationship between kinetic energy and potential energy of the system. The drift coefficients and diffusion coefficients are averaged with respect to the period of θ. When the excitation frequency is in the lock-in field, large parametric rolling appears. The stationary probability density function (PDF) of the roll angle obtained by solving the Fokker-Planck-Kolmogorov (FPK) equation compares well with Monte Carlo simulation in the lock-in field. The improved method can relax the limitation of broad-band excitation required by stochastic averaging method. It can also consider both the nonlinear damping and nonlinear restoring force of roll motion. Therefore, the improved method is an efficient way to calculate the nonlinear roll response of ships in real sea conditions.

Effects of outrigger configuration on trimaran stability in longitudinal waves

A trimaran has excellent characteristics of transverse stability and less resistance because of its unconventional multiple slender hull form. However, the multi-hull configuration potentially triggers parametric roll due to the periodical fluctuation of metacentric height. In this study, an efficient numerical model was established to investigate the effects of the outriggers on trimaran stability in longitudinal waves, based on Froude-Krylov assumption and hydrostatic assumption. Then, the relationship between the metacentric height of the trimaran and the outrigger position was discussed, and the influence of heave/pitch motion responses on the wave stability of the trimaran was evaluated. Furthermore, a method of predicting the stability zone was proposed and checked by numerical simulation based on computational fluid dynamics. The relationship between the outrigger position and the potential risk of the parametric roll was analyzed by the obtained stability zones. It was found that the decrease in the outrigger displacement ratio and the increase in the clearance can significantly raise the risk of parametric roll of a trimaran.

New extreme statistics strategy for the extreme value predictions of ship parametric rolling motions through limited model test observations

This work proposes a new extreme statistics strategy to predict the extreme parametric rolling angle through minimal observations from model tests. The core of this strategy is a new synthetic moment method. Based on the Hermite transformation and the Markov chain, the synthetic moment method can provide extreme value predictions for stationary processes. Besides, this work introduces one specific simplification to solve the problem induced by the non-stationarity of the parametric roll. With the help of the new extreme statistics strategy, this work obtains the CDF and PDF of the extreme parametric rolling angle for the C11 container ship. These predictions are derived from only one observed model test time history. The data statistics of other model tests and a vast amount of numerical simulations verify the validities of these predictions. Compared with other methods, the new strategy shows advantages for small sampling predictions. It is possible to replace the widely used ACER method in case of insufficient samples. In addition, further research confirms that the new strategy's intrinsic probability model differs from the widely used GEV model, which is more reasonable for extreme value predictions in a finite time range. The newly presented strategy should effectively predict the extreme value for other complicated stochastic responses.

Deep learning machine based ship parametric rolling simulation and recognition algorithms

In this work, we propose a “grey box” algorithm consisting of a deep learning network and parametric roll equation to provide the parametric roll simulations. A basic unsupervised method——principal component analysis is introduced into this algorithm to improve efficiency and accuracy. Besides, it has been proved that different wave time histories generated by the same wave spectrum will induce very different parametric rolling behaviors. Thus, we also proposed an algorithm that combines the deep learning method with spectral analysis to recognize the wave time histories that induce large amplitude rolling. A convolution layer and a pooling layer are added to the recognition network to reduce the input dimension. Besides, according to our study of training methods, we have found that extreme learning machine performs much better than back propagation network. Using the principal component analysis technique and the “grey box” based extreme learning machine, we can obtain very accurate simulations of the parametric roll of the C11 container ship in a short time. Besides, by using the spectral analysis and the extreme learning machine with convolution and pooling layer, we can accurately recognize the time histories induce large-amplitude parametric roll of the C11 container ship.

Real-Time Identification of Parametric Roll

_ The International Maritime Organization (IMO) provides criteria to assess the vulnerability of ships toward the phenomenon of parametric roll. Such long-term vulnerability assessments permit to qualify statistically the ships vulnerability regarding parametric roll. However, it does not permit to assess the risk of parametric roll in real time. Thus, researchers and private company have developed methods and software to evaluate this risk using the real-time ship motions provided by the onboard inertial unit. Those methods detect parametric roll events when it appears and warn the officer of the watch of the immediate danger. This paper presents an innovative real-time detection method and its validation. The detection method considers physical conditions required for parametric roll to appear. Especially, it considers the coupling between the roll and pitch motions. The method and its associated parametric roll alarm are entirely described. The results show that the method correctly identifies parametric roll in regular longitudinal waves and do not lead to false detection in regular beam waves. A statistical study in irregular waves based on simulated data presents very promising results with a parametric roll detection rate in head seas above 80% when heavy roll motions appear and a false detection rate in beam seas below 4%. Finally, a 2.5-day full-scale validation on a container ship provides promising results. Introduction The container ships, with typical hull shape presenting flat stern and pronounced bow flare, are especially subject to parametric roll. Operationally, several accidents which have led to the loss of containers at sea may be imputed to this phenomenon (France et al. 2003; Carmel 2006; MAIB 2020; DMAIB 2022). Following the accidents of the C11-class container ship (France et al. 2003) and of the Maersk Carolina (Carmel 2006), both due to parametric roll, insurers asked the shipowners to take measures to avoid such failure to appear (Dølhie 2006). Two solutions are rapidly developed to answer this request. The first one is developed by SeaSense and named SeaSense Monitoring (Nielsen et al. 2006).

Influence of sea areas and season in navigation on the ship vulnerability to the parametric rolling failure mode

The influence of areas and season in navigation on the ship vulnerability to the parametric rolling failure mode is investigated. The second check of level 2 vulnerability criterion, defined in the interim guidelines on the second generation intact stability criteria (SGISC), is used for the assessment of ship vulnerability to the parametric rolling failure mode. In the framework of SGISC, even ships failing to pass the vulnerability criteria are allowed to operate by implementing the operational limitations. In order to prepare operational limitations related to areas or routes, and season, area-specific and season-specific wave scatter tables are made using Global Wave Statistics. Service speed and major navigation routes/areas of containerships and pure car and truck carriers are determined by analysing global satellite AIS data. Then, the vulnerability is assessed for a C11 class containership and a pure car and truck carrier for the determined limited navigation areas to identify the failure risk depending on the sea areas. Further, the effect of seasonality on the risk of stability failure due to parametric rolling is discussed.

An alternative methodology for the simplified operational guidance in the framework of second generation intact stability criteria

Within the framework of the second-generation intact stability criteria (SGISc), a procedure to provide simplified operational guidance (OG) has been proposed. In particular, the phenomenon of parametric rolling has been investigated. The proposed methodology is meant to be an intermediate level between the suggested simplified OG and the deterministic OG, as defined in the MSC.1/Circ.1627. The proposed guidance relies on a simplified numerical tool able to assess ship roll motion due to non-linear irregular wave effects in the time domain. Outcomes are elaborated in the post-process phase, taking the maximum roll angle as leading criterion. Once defined the structure of this tool, an application has been carried out to a representative model of post-panamax container vessel. As benchmark study, the results have been compared to those obtained by the application of MSC.1/Circ.1228 and MSC.1/Circ.1627 (simplified OG) by means of polar diagram representation. Outcomes have been discussed and a general agreement can be found between the simplified OG and the proposed one. Although, it appears that the latter can detect dangerous roll motion for a more comprehensive set of sailing condition.