Moving-Particle Semi-Implicit Method for Vortex Patterns and Roll Damping of 2D Ship Sections

A meshless method, Moving-Particle Semi-hnplicit Method （MPS） is presented in this paper to simulate the rolling of different 2D ship sections. Sections S. S. 0.5, S.S. 5.0 and S. S. 7.0 of series 60 with CB = 0.6 are chosen for the simulation. It shows that the result of MPS is very close to results of experiments or mesh-numerical simulations. In the simulation of MPS, vortices are found periodically in bilges of ship sections. In section S. S. 5.0 and section S. S. 7.0, which are close to the middle ship, two little vortices are found at different bilges of the section, in section S. S. 0.5, which is close to the bow, only one big vortex is found at the bottom of the section, these vortices patterns are consistent with the theory of Ikeda. The distribution of shear stress and pressure on the rolling hull of ship section is calculated. When vortices are in bilges of the section, the sign clmnge of pressure can be found, but in section S. S. 0.5, there is no sign change of pressure because only one vortex in the bottom of the section. With shear stress distribution, it can be found the shear stress in bilges is bigger than that at other part of the ship section. As the free surface is considered, the shear stress of both sides near the free surface is close to zero and even sign changed.

Vortex Patterns and Roll Damping on Various Cross Sections of Ships

A numerical study is presented on roll damping of ships by solving Navier-Stokes equation. Two Dimensional unsteady incompressible viscous flow around the rolling cylinders of various ship-like cross sections are numerically simulated by use of the computational scheme previously developed by the authors. The numerical results show that the location of the vortices is very similar to the existing experimental result. For comparison of vortex patterns and roll damping on various ship-like cross sections, various distributions of shear stress and pressure on the rolling ship hull surface are presented in this paper. It is found that there are two vortices around the midship-like section and there is one vortex around the fore or stern section. Based on these simulation results, the roll damping of a ship including viscous effects is calculated. The contribution of pressure to the roll moment is larger than the contribution of frictional shear stress.

A Simple Prediction Formula of Roll Damping of Conventional Cargo Ships on the Basis of Ikeda＇s Method and Its Limitation

Since the roll damping of ships has significant effects of viscosity, it is difficult to calculate it theoretically. Therefore, experimental results or some prediction methods are used to get the roll damping in design stage of ships. Among some prediction methods, Ikeda＇s one is widely used in many ship motion computer programs. Using the method, the roll damping of various ship hulls with various bilge keels can be calculated to investigate its characteristics. To calculate the roll damping of each ship, detailed data of the ship are needed to input. Therefore, a simpler prediction method is expected in primary design stage. Such a simple method must be useful to validate the results obtained by a computer code to predict it on the basis of Ikeda＇s method, too. On the basis of the predicted roll damping by Ikeda＇s method for various ships, a very simple prediction formula of the roll damping of ships is deduced in the present paper. Ship hull forms are systematically changed by changing length, beam, draft, mid-ship sectional coefficient and prismatic coefficient. It is found, however, that this simple formula can not be used for ships that have high position of the center of gravity. A modified method to improve accuracy for such ships is proposed.

Estimation of Nonlinear Roll Damping by Analytical Approximation of Experimental Free-Decay Amplitudes

Damping is critical for the roll motion response of a ship in waves. A common method for the assessment of damping in a ship’s rolling motion is to perform a free-decay experiment in calm water. In this paper, we propose an approach for estimating nonlinear damping that involves a linear exponential analytical approximation of the experimental roll free-decay amplitudes, fol- lowed by parametric identification based on the asymptotic method. The restoring moment can be strongly nonlinear. To validate this method, we first analyzed numerically simulated roll free-decay data using rolling equations with two alternative parametric forms: linear-plus-quadratic and linear-plus-cubic damping. By doing so, we obtained accurate estimates of nonlinear damping coefficients, even for large initial roll amplitudes. Then, we applied the proposed method to real free-decay data obtained from a scale model of a bulk barrier, and found the simulated results to be in good agreement with the experimental data. Using only free-decay peak data, the proposed method can be used to estimate nonlinear roll-damping coefficients for conditions with a strongly nonlinear restoring moment and large initial roll amplitudes.

Rudder Roll Damping Autopilot Using Dual Extended Kalman Filter–Trained Neural Networks for Ships in Waves

The roll motions of ships advancing in heavy seas have severe impacts on the safety of crews,vessels,and cargoes;thus,it must be damped.This study presents the design of a rudder roll damping autopilot by utilizing the dual extended Kalman filter(DEKF)trained radial basis function neural networks(RBFNN)for the surface vessels.The autopilot system constitutes the roll reduction controller and the yaw motion controller implemented in parallel.After analyzing the advantages of the DEKF-trained RBFNN control method theoretically,the ship’s nonlinear model with environmental disturbances was employed to verify the performance of the proposed stabilization system.Different sailing scenarios were conducted to investigate the motion responses of the ship in waves.The results demonstrate that the DEKF RBFNN based control system is efficient and practical in reducing roll motions and following the path for the ship sailing in waves only through rudder actions.

Direct calculation method of roll damping based on three-dimensional CFD approach

The effect of roll damping on the prediction of a ship＇s motion is significant. A method based on the 3-D CFD approach for calculating the roll damping of a ship is proposed in this paper. The free decay experiments of 4 different types of ships at zero velocity are carried out. The roll damping coefficients are calculated and compared with the experiment results, with a good agreement. It is shown that the method adopted in this paper could be used to simulate the free rolling of a ship in the calm water at zero velocity very well and with good, stable accuracy for the prediction of the roll damping, and also with good applicability. This method may be further developed for the prediction of a full scale ship in the future.

Nonlinear roll damping of a barge with and without liquid cargo in spherical tanks

Damping plays a significant role on the maximum amplitude of a vessel’s roll motion,in particular near the resonant frequency.It is a common practice to predict roll damping using a linear radiation-diffraction code and add that to a linearized viscous damping component,which can be obtained through empirical,semi-empirical equations or free decay tests in calm water.However,it is evident that the viscous roll damping is nonlinear with roll velocity and amplitude.Nonlinear liquid cargo motions inside cargo tanks also contribute to roll damping,which when ignored impedes the accurate prediction of maximum roll motions.In this study,a series of free decay model tests is conducted on a barge-like vessel with two spherical tanks,which allows a better understanding of the nonlinear roll damping components considering the effects of the liquid cargo motion.To examine the effects of the cargo motion on the damping levels,a nonlinear model is adopted to calculate the damping coefficients.The liquid cargo motion is observed to affect both the linear and the quadratic components of the roll damping.The flow memory effect on the roll damping is also studied.The nonlinear damping coefficients of the vessel with liquid cargo motions in spherical tanks are obtained,which are expected to contribute in configurations involving spherical tanks.

Advances on numerical and experimental investigation of ship roll damping

This paper presents recent developments towards efficient and reliable methods for roll damping estimation based on numerical simulations as well as model tests using the harmonic excited roll motion(HERM)technique.A newly designed automatic roll damping estimation procedure shows the advantage of a just-in-time post processing of experimental measurement results.Real-time analysis of the measured roll damping values permits a considerable shortening of the test times.Thus,a large number of investigations can be carried out with relatively manageable effort in order to determine the roll damping behavior of different keel configurations or at operating conditions,e.g.,different sized keels or Froude numbers.In addition,HERM measurement method is applied to investigate the memory effect.For this purpose,different excitation schemes are introduced and the results are analyzed.Moreover,a study of the scale effect on the roll damping properties is conducted,in which experimental and numerical investigations are performed for two scales of a ship model.Furthermore,a method is developed that significantly reduces the effort of Reynolds average Navier-Stokes(RANS)-based simulations of roll motion.The reduction of simulation time is achieved by introducing an artificial damping.The obtained results show that the developed method is very well applicable for numerical as well as in experimental investigations.During the model tests using HERM technique,the model is free and the rudder is used to keep the straight-ahead course.The analysis of the numerical and experimental results shows that the influence of the rudder induced force and moment during HERM tests is not negligible and the contribution of the rudder must be taken into account by estimating the roll damping.Finally,a new concept is developed to investigate the parametric roll behavior of ships,which allows neglecting the consideration of the complex modelling of free surface waves in the simulations.During the RANS computations,a potential-based method is applied to compute the variation of restoring terms due the roll motion.

Experimental Investigation into the Effect of Roll Amplitude on Roll Damping

An in-house large eddy simulation(LES)code has been developed in the previous study.In order to validate the code for simulation of roll motion,effect of roll amplitude on forced roll damping is experimentally investigated in a circulating water channel at Shanghai Jiao Tong University(SJTU).KRISO very large crude carrier 2(KVLCC2)is taken as a target ship,and a model with a scale of 1:128.77 is manufactured.Tests are carried out for the ship model at shallow draft with frequencies around its natural roll frequency,where natural roll frequency is attained via free roll decay.Six forced roll tests with roll amplitudes ranging from 1?to 4?are performed experimentally,and three forced roll motions are simulated with the in-house LES code for middle section of the ship model.Discrepancies between the computed roll damping coefficients and the ones from forced roll tests are quite small.By means of particle image velocimetry(PIV),velocity fields in the vicinity of the ship model,and generation and evolution of vortices near the ship bilge are measured in detail.It is shown that roll amplitude has a significant effect on the vortex behavior,and therefore on the magnitude of roll damping coefficient.Further experimental and numerical investigation into roll motions with large amplitudes is planned.

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.