Prediction Of Parametric Rolling Research Articles

Parametric roll prediction of the KCS containership in head waves with emphasis on the roll damping and nonlinear restoring moment

The quantitative prediction of parametric roll of a KCS containership are conducted using a 5-DOF nonlinear time domain model based on the potential flow. In the model, linear radiation and diffraction forces are calculated by the STF method and transferred into time domain using IRF approach, while nonlinear restoring and F–K forces are calculated through pressure integration over instantaneous wetted surfaces. Roll damping is estimated using the Ikeda's method. The sensitive analysis on roll damping is conducted. Five different models for nonlinear restoring and F–K forces are discussed.It is confirmed that the five models overestimate the parametric roll amplitude. Model A considering only the nonlinearity of restoring forces caused by instantaneous ship position under still water is suitable for parametric roll prediction among five models. Moreover, accurate estimation of pitch motions is vital for parametric roll prediction. Through the sensitive analysis, it is found that roll damping affects parametric roll amplitudes but has no effect on the speed region where parametric roll occurs. The sensitivity of nonlinear quadric damping against parametric roll is small, while the sensitivity of linear damping is large. The sensitivity of roll damping against parametric roll for cases close to the speed threshold is significant.

Study on Roll Restoring Arm Variation Using a Three-Dimensional Hybrid Panel Method

Providing a reliable numerical tool for the prediction of parametric roll and pure loss of stability is a difficult task. It is acknowledged that the occurrence of these two failure modes is mainly attributed to the variation of roll restoring arm, which should be calculated accurately. This work studies exclusively the roll restoring arm variation numerically and experimentally. First, partially restrained experimental tests at different constant heeling angles (up to 30°) are conducted to measure the variation of roll restoring arm in regular waves. Second, a numerical method for the calculation of roll restoring arm in waves taking radiation and diffraction moments into account is adopted. The calculation results are benchmarked against experimental model test data. Third, the characteristics of roll restoring arm variation and the effects of radiation and diffraction moments on roll restoring arm variation (GZRD) in head and following seas are investigated. Finally, the feasibility of GZ calculated by the integral of instantaneously average wetted surface is studied by comparing the results with that calculated by the integral of the fully instantaneously wetted surface. The research show that the GZRD can be ignored in following seas. The GZ in head seas consists of two important harmonic components, and GZRD is the main contribution of the second harmonic component. Therefore, GZRD should be calculated with consideration of the instantaneous heeling angles and Froude number in head seas, especially for the prediction of large amplitude roll motion at high speed. 1. Introduction Currently, the second-generation intact stability criteria are under development by the International Maritime Organization (IMO) (IMO SLF 53/WP.1-Add.1 2011; IMO SDC 3/WP.5 2016). Five different kinds of potentially dangerous dynamic stability failure modes in waves were proposed. Parametric roll and pure loss of stability are two of the stability failure modes that may lead to capsizing of a ship. According to the proposed drafts, a multilevel structure was adopted to make sure that numerical assessment procedures are only applied when the vulnerability to dynamical stability failures is beyond reasonable doubt. Assessment of the vulnerability criteria is normally based on simplified geometry characteristics or empirical formulas. However, direct stability assessment requires highly accurate prediction (Kobylinski 2012).

Effects of radiation and diffraction forces on the prediction of parametric roll

Parametric roll is an important stability failure mode in the second generation intact stability criteria, which are currently under development by International Maritime Organization (IMO). The roll restoring arm, which is one of the dominating factors for the prediction of parametric roll, should be calculated preciously. In this paper, firstly, the effects of the radiation and diffraction forces on the roll restoring arm (GZR&D) under different heeling angles and wave amplitudes are studied based on the body exact method, in which all the hydrodynamic forces are calculated by integrating wave pressure up to the wave surface. Secondly, the effects of radiation and diffraction forces on parametric roll are studied by the direct simulation using a coupled heave-roll-pitch model based on the three dimensional mixed source method. Finally, by taking one passenger ship as an example, the calculation accuracy of the body exact method is compared with the commonly used body linear method. The results show that the effect of radiation and diffraction forces on righting arm variation has nonlinear relationships with heeling angles and wave amplitudes, and the body exact method can provide more accurate prediction results for parametric roll in head waves than the body linear method. Therefore, the nonlinear effects of instantaneous roll angles and wave amplitudes on GZR&D variation in waves should be considered for the prediction of parametric roll in head waves.

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.

Prediction of parametric rolling of ships in single frequency regular and triple frequency group waves

A 3D nonlinear time domain simulation method based on the impulse response function concept is applied to the investigation of parametric rolling of the ITTC-A1 containership. In the numerical simulation, the hydrodynamic coefficients are determined beforehand by a 3D frequency domain panel code on the basis of linear potential theory, whereas the most nonlinear terms in the equations of motion are taken into account, such as the excitation by large amplitude waves (exact Froude–Krylov forces/moments), exact restoring forces/moments resulting from integration of the hydrostatic pressures over the actually wetted surface of the ship and the semi-empirical nonlinear viscous damping correction. In addition, all nonlinear inertia terms are retained when considering solution of large amplitude motions. The parametric rolling is predicted by solving the 6 degrees of freedom (DoF) nonlinear equations of ship motion in the time domain in response to single frequency regular waves and triple frequency group waves. The obtained numerical results are compared with corresponding experimental measurements and numerical predictions of an earlier conducted international benchmark study proving the good performance of the developed method in terms of the predictability of parametric roll phenomena and to a lesser degree to the accuracy of predicted roll amplitude values.

Development of a semi-analytical method for the efficient prediction of parametric roll

A semi-analytical approach to the simulation of the parametric roll motions of container ships in head seas is presented. In the proposed 1.5-degree of freedom model, the nonlinear change in the transverse stability induced by the vertical motions and wave elevation is approximated by investigating the relationship between the restoring lever (GZ) and the metacentric height (GM) in waves. In particular, the variations in the GM in irregular waves are modeled by the transfer functions of the mean value and first harmonic component on the basis of the assumption of superposition. Using the derived formula, the quantitative prediction of parametric roll motion as well as the susceptibility to such motion in regular and irregular waves is conducted. A comparison with the results of a weakly nonlinear time-domain method, namely, the impulse response function method based on the hydrodynamic coefficients of strip theory, is carried out to validate the proposed model. Not only the accuracy and efficiency of the present approach but also the stochastic properties of parametric roll in random seas are examined considering the sensitivities and uncertainties in the computations.

Prediction of parametric rolling in waves with a time domain non-linear strip theory model

A time-domain non-linear strip theory model of ship′s motions in six degrees-of-freedom is described and is validated by comparing numerical predictions with experimental results of parametric rolling of a containership. The calculation of the time variations of the restoring force is made using a pressure integration technique over the instantaneous submerged hull. Hydrodynamic effects are based on a potential flow strip theory using Frank′s Close fit method. A semi-empirical formulation is adopted for the surge motion. Different models for roll damping have been introduced so far in the governing equations but in the present case roll damping is determined directly from experimental data that includes roll decay tests with different forward speed, which allows the assessment of the effect of ship speed on roll damping. Comparisons between numerical and experimental results demonstrate the usefulness and accuracy of the method proposed.

規則波中パラメトリック横揺れの定量的数値予測に関する研究

Since parametric roll is well known as one of the most dangerous phenomena which could lead to serious accidents due to large amplitude roll motion, a new Intact Stability code, which is under development at IMO, is required to cover this phenomena. To realize quantitative prediction of parametric roll, systematic forced roll motion tests were conducted to measure roll restoring variation and roll damping with relevant roll angle/amplitude up to 30 degrees. Then, a 3DOF numerical model based on nonlinear strip method is developed and compared with model experiment to validate its prediction accuracy and applicability as a direct assessment method towards the new Intact Stability code.

Prediction potential of the parametric rolling behaviour of a post-panamax containership

A systematic investigation on the prediction of parametric rolling exhibited by a post-panamax containership is described, on the basis of several techniques. Analytical formulae that appear in current industrial guidelines are evaluated in a step-by-step process against various numerical predictions. The method of continuation of nonlinear dynamics is introduced in order to expedite the identification of the instability boundary and the prediction of steady amplitudes of roll oscillation. A well-known panel code is shown to be capable of reproducing parametric roll growth.

A theoretical and experimental investigation of indirectly excited roll motion in ships

The phenomenon of indirectly exciting the roll motion of a vessel due to nonlinear couplings of the heave, pitch and roll modes is investigated theoretically and analytically. Two nonlinear mechanisms that cause large-amplitude rolling motions in a head or following sea are investigated. The first mechanism is internal or autoparametric resonance and the second is parametric resonance. The energy put into the pitch and heave modes by the wave excitations may be transferred into the roll mode by means of nonlinear coupling among these modes; thus, the roll can be indirectly excited. As a result, a ship in a head or following sea can spontaneously develop severe rolling motion. In the analytical approach, the method of multiple scales is used to determine a system of nonlinear first-order equations governing the modulation of the amplitudes and phases of the system. The fixed-point solutions of these equations are determined and their bifurcations are investigated. Hopf bifurcations are found in the case of two-to-one internal resonance. Numerical simulations are used to investigate the bifurcations of the ensuing limit cycles and how they produce chaos. Experiments are conducted with tanker and destroyer models. They demonstrate some of the nonlinear effects, such as the jump phenomenon, the subcritical instability, and the coexistence of multiple solutions. The experimental results are in good qualitative agreement with the results predicted theoretically.