Experimental and Numerical Investigations of Ship Parametric Rolling in Regular Head Waves

Parametric rolling is one of five types of the ship stability failure modes as proposed by IMO. The periodic change of the metacentric height is often considered as the internal cause of this phenomenon. Parametric rolling is a complex nonlinear hydrodynamic problem, often accompanied by large amplitude vertical motions of ships. In recent years,the Reynolds-averaged Navier–Stokes(RANS) equation simulations for viscous flows have made great progress in the field of ship seakeeping. In this paper, the parametric rolling for the C11 containership in regular waves is studied both experimentally and numerically. In the experiments, parametric rolling amplitudes at different drafts, forward speeds and wave steepnesses are analyzed. The differences in the steady amplitudes of parametric rolling are observed for two drafts. The effect of the incident wave steepness(or wave amplitude) is also studied, and this supports previous results obtained on limits of the stability for parametric rolling. In numerical simulations, the ship motions of parametric rolling are analyzed by use of the potential-flow and viscous-flow methods. In the viscousflow method, the Reynolds-averaged Navier–Stokes equations are solved using the overset grid method. The numerical accuracies of the two methods at different wave steepnesses are also discussed.

Studies on Stochastic Parametric Roll of Ship with Stochastic Averaging Method

The paper studies the parametric stochastic roll motion in the random waves.The differential equation of the ship parametric roll under random wave is established with considering the nonlinear damping and ship speed.Random sea surface is treated as a narrow-band stochastic process,and the stochastic parametric excitation is studied based on the effective wave theory.The nonlinear restored arm function obtained from the numerical simulation is expressed as the approximate analytic function.By using the stochastic averaging method,the differential equation of motion is transformed into Ito’s stochastic differential equation.The steady-state probability density function of roll motion is obtained,and the results are validated with the numerical simulation and model test.

Ince-Strutt Stability Charts for Ship Parametric Roll Resonance in Irregular Waves

Ince-Strutt stability chart of ship parametric roll resonance in irregular waves is conducted and utilized for the exploration of the parametric roll resonance in irregular waves. Ship parametric roll resonance will lead to large amplitude roll motion and even wreck. Firstly, the equation describing the parametric roll resonance in irregular waves is derived according to Grim’s effective theory and the corresponding Ince-Strutt stability charts are obtained. Secondly, the differences of stability charts for the parametric roll resonance in irregular and regular waves are compared. Thirdly, wave phases and peak periods are taken into consideration to obtain a more realistic sea condition. The influence of random wave phases should be taken into consideration when the analyzed points are located near the instability boundary. Stability charts for different wave peak periods are various. Stability charts are helpful for the parameter determination in design stage to better adapt to sailing condition. Last, ship variables are analyzed according to stability charts by a statistical approach. The increase of the metacentric height will help improve ship stability.

Vibration energy harvesting for low frequency using auto-tuning parametric rolling pendulum under exogenous multi-frequency excitations

An electromagnetic parametrically excited rolling pendulum energy harvester with self-tuning mechanisms subject to multi-frequency excitation is proposed and investigated in this paper.The system consists of two uncoupled rolling pendulum.The resonance frequency of each the rolling pendulum can be automatically tuned by adjusting its geometric parameters to access parametric resonance.This harvester can be used to harvest the energy at low frequency.A prototype is developed and evaluated.Its mathematical model is derived.A cam with rolling follower mechanism is employed to generate multi-frequency excitation.An experimental study is conducted to validate the proposed concept.The experimental results are confirmed by the numerical results.The harvester is successfully tuned when the angular velocity of the cam is changed from 1.149 to 1.236 Hz.

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.

不同装载条件下小型渔船参数横摇的非定常RANS CFD仿真

Fishing boats have unique features that make them prone to changing loading conditions.When the boat leaves the port,the empty fish tank gradually fills up during fishing operations which may result in parametric roll(PR).This dangerous phenomenon that can lead to capsizing.The present study aims to understand better the behaviour of parametric roll in fishing boats and its relation to changing loading conditions.The study considers the effects of displacement and the GM/KM ratio on parametric roll,as well as the longitudinal flare distribution at the waterline.Two assessments to detect the parametric roll occurrence in early stage were carried out by using the level 1 assessment of parametric roll based on the Second Generation of Intact Stability criteria(SGIS)from International maritime Organisation(IMO)and the Susceptibility criteria of Parametric roll from the American Bureau of Shipping(ABS).Then,the CFD method is used to predict the amplitude of the parametric roll phenomenon.The results provide important insights to fishing vessel operators on how to manage loading conditions to maintain stability and avoid hazardous situations.By following the guidelines outlined in this study,fishing boats can operate more safely and efficiently,reducing the risk of accidents and improving the overall sustainability of the fishing industry.

Ship Roll Analysis Using CFD-Derived Roll Damping:Numerical and Experimental Study

This study investigates the roll decay of a fishing vessel by experiments and computational fluid dynamics(CFD)simulations.A fishing vessel roll decay is tested experimentally for different initial roll angles.The roll decay is also simulated numerically by CFD simulations and is validated against the experimental results.It shows that the roll damping could be obtained by CFD with high level of accuracy.The linear and nonlinear damping terms are extracted from the CFD roll decay results and are used in a potential-based solver.In this way we are using a hybrid solver that benefits the accuracy of the CFD results in terms of roll damping estimation and the fast computations of the potential-based solver at the same time.This hybrid method is used for reproducing the free roll decays at Fn=0 and also in analyzing some cases in waves.The experiments,CFD and the hybrid parts are described in detail.It is shown that the suggested method is capable of doing the simulations in a very short time with high level of accuracy.This strategy could be used for many seakeeping analyses.

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 KG_(max) 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 KG_(max) 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 KG_(max) 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 KG_(max) curves. In consequence, it is not sufficient to check that C2 is lower than the maximum authorized value(R_(PR0)) for a fixed ship's loading condition.