Time-domain Rankine Panel Method Research Articles

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.

Study on ship operation performance in actual seaways using time-domain free-running simulation

This study considers the evaluation of ship operational performance in real sea states using a time-domain approach. The current seakeeping-maneuvering coupling approach consists of two modules. First, in the seakeeping module, the time-domain three-dimensional Rankine panel method is applied to compute wave-induced forces and resultant ship motion. To validate this module, the computational results for wave drift force are compared with the existing experimental data for various forward speeds and regular wave conditions. Second, in the maneuvering module, the equations of motion with 4 degrees of freedom that are based on the Maneuvering Modeling Group are solved to simulate the ship navigation. The computed seakeeping and maneuvering values are immediately transferred between the two modules in the time domain, and so they are directly integrated. By applying this coupling method, a free-running simulation for a ship navigating along a given route is performed. The trajectory tracking method based on a proportional–derivative-based rudder control is adopted for straight course-keeping. Not only the speed loss but also the attitude for route maintenance is evaluated for various environmental load conditions. The simulation results are validated by a comparison with those of the existing free-running model test. Based on comparisons, environmental load effects and resultant quantities on operational performance are discussed.

Numerical study on wave-induced motions and steady wave drift forces for ships in oblique waves

This paper considers numerical predictions of wave-induced motions and steady wave drift forces for ships in oblique waves. The velocity potential around the ship is computed via a time domain Rankine panel method. Based on the computed velocity potential, the six degree of freedom wave-induced motions were computed and then the second order wave loads were evaluated using a near field method. An artificial soft spring system was employed to control horizontal ship motions. The steady longitudinal and transverse wave drift forces and the steady yaw moment were computed for the KVLCC2 tanker at zero forward speed and for the S-175 containership at constant forward speed. Predicted results generally compared favorably to published experimental measurements. A systematic analysis of the effects of the soft spring system on wave-induced motions and steady wave drift forces demonstrated that, although the increased stiffness of the system changed the corresponding motion response of the ships, a spring's influence was negligibly small if its stiffness was weak enough.

Study on steady flow approximation in turning simulation of ship in waves

This study considers the effects of steady flow approximation in the analysis of ship maneuvering in waves. To this end, the ship motion due to waves is analyzed using the three-dimensional time-domain Rankine panel method, and the wave drift forces acting on a ship are calculated by applying the near-field method to directly integrate the pressure on the hull surface. In this seakeeping analysis, the steady flow induced by the operation velocity of the ship is approximated by a uniform flow or double-body flow. The ship maneuvering in waves not only advances forward but also drifts and rotates; hence, it can be regarded as a lifting body. Therefore, the vortex flow generated at the sharp end of the hull is also modeled and reflected in the steady-flow approximation. In order to investigate how the seakeeping performance is determined according to the approximation method, ship motions and drift forces induced by waves are computed for the ship moving forward or obliquely. Lastly, the numerical simulation for the turning test in a regular wave is performed based on the time-domain direct coupling method. Based on the accuracies of computation results compared with existing experimental data, the steady-flow induced coupling effects between seakeeping and maneuvering quantities are discussed.

Numerical prediction of wave added resistance using a Rankine Panel method

Based on a time domain Rankine panel method, a computer code was developed to predict wave added resistance. The unknown variables of the discretized flow field boundaries were represented using the quadratic B-spline basis function; the temporal derivative of the free surface conditions were approximated using an Euler scheme. The added resistance was computed via a near-field method. Three numerical approaches were introduced, namely, choosing the boundary end condition, neglecting the second order derivative of the disturbed potential, and computing the water line integral. Numerical computations were conducted in short and long waves for a Wigley hull, the S-175 container ship, and the KVLCC2 tanker. The double-body linearization and the Neumann–Kelvin linearization were tested, and numerical results were compared to published experimental measurements and numerical data. Fairly good agreement was found between the results of double-body linearization and the published data. Effects of wave radiation and diffraction on added resistance were analyzed, demonstrating that the interaction between radiation and diffraction should not be omitted in long waves.

On the development of a higher order time-domain Rankine panel method for linear and weakly non-linear seakeeping computations

The development of a numerical method for the computation of the linear and weakly non-linear wave effects on floating bodies is presented. The method is formulated in terms of a higher order time-domain boundary elements method based on the Rankine sources. The higher order approach is assumed for both body geometry (using NURBS) and computed function (using B-splines), the former in a standard CAD geometry format to provide more flexibility. In this paper, the procedures adopted for the numerical solution of the main mathematical problems involved are thoroughly described and discussed, with the purpose of documenting important aspects of these methods that are often absent in the literature. Several verification cases are presented, including first-order quantities (motion RAOs, velocity field, and free-surface elevation) and second-order loads (mean drift, sum, and difference components). Regarding the latter, at the present stage of the development, the numerical method is able to compute the so-called quadratic components of forces and moments. For these loads, steady-state solutions in both monochromatic and bichromatic waves are compared to the results obtained with a well-known frequency-domain code.

Study on added resistance of a ship under parametric roll motion

Parametric roll of ship is a rare event occurring in specific conditions, but it can cause the dynamic roll instability. Since this phenomenon is dependent on ship speed and wave frequency, the development of roll motion and the resultant added resistance which can cause speed change should be considered simultaneously when parametric roll occurs. This paper considers a numerical study on the added resistance of a modern containership under parametric roll. A time-domain Rankine panel method adopting a weakly nonlinear formulation is adopted to obtain ship motions and added resistances in waves. Seakeeping computations in regular head-sea conditions are performed with and without parametric roll, and the increment of added resistance is investigated with regard to the components classified in the direct pressure integration method. Furthermore, according to the decoupling phenomena between the components of the vertical motions and the roll motion, a correlation between the parametric roll and the added resistance is derived. Lastly, a simple prediction method for the added resistance in irregular parametric roll motion is suggested based on the correlation, and its accuracy and efficiency are discussed by comparing the prediction with the results of the direct numerical computation.

A study on prediction of ship maneuvering in regular waves

A simulation method is developed for predicting ship maneuvering in regular waves. Based on a two-time scale model, the total ship motion is divided into the low frequency maneuvering motion and the high frequency wave-induced motion. The maneuvering analysis is based on a MMG model which takes the mean second-order wave loads into account. In order to evaluate the second-order wave loads, a velocity potential is introduced and decomposed into a basic part and a perturbation part, which are related to the maneuvering motion and the wave-induced motion, respectively. The basic part is evaluated based on the double-body model with a trailing vortex sheet, while the perturbation part is solved via a time domain Rankine panel method. The effects of maneuvering motion on the wave forces are considered through the m-terms as well as the leading-order terms kept in the boundary conditions on the free surface. By using the proposed method, turning and zig-zag maneuvers of the S-175 container ship in regular waves are simulated. The predicted turning trajectories and 10°/10° and 20°/20° zig-zag maneuvers are compared with the experimental data, which show fairly good agreements. The drift forces and moment on the ship turning in waves are also discussed.

A new time domain Rankine panel method for simulations involving multiple bodies with large relative displacements

Many important offshore operations involve multiple vessels whose relative positions change considerably in the course of the operational procedures. When the action of sea waves on the dynamics of these vessels is concerned, an accurate modeling of the hydrodynamic problem is not an easy task. The use of frequency-domain panel codes is compromised by the variations of the bodies’ relative positions and may lead to inconsistent results. A time-domain approach is clearly more appropriate, but even in this case the representation of the moving bodies requires a re-meshing procedure and considerable computational efforts. This paper addresses the problem of wave interaction with multiple bodies with large relative displacement by integrating a re-meshing procedure to a time-domain Rankine panel code. The mathematical algorithms adopted for generating the new free-surface grids and performing the interpolation of wave elevation and velocity potential are described in detail. The paper also presents a set of dedicated captive model tests performed in a wave basin as a means of verifying the performance of the numerical method. Tests involved models with simple geometries that performed slow prescribed drift motions in the presence of incoming regular waves. Hydrodynamic forces were measured on one of the models and different levels of transient interaction effects could be reached by varying the frequency ratios between waves and body motions. The good performance of the method is then attested by directly comparing the hydrodynamic forces predicted by the computational code with those measured during the model tests. Moreover, it will be shown that the numerical model was able to capture some interesting Doppler effects that will be discussed together with other validation results.

Time domain simulations of radiation and diffraction by a Rankine panel method

The radiation and the diffraction of a ship with a forward speed are studied by using a time domain Rankine panel method. The free surface conditions are linearized onto an undisturbed free surface based on the double body flow. The linearized body boundary condition is applied on the mean wetted hull surface. The fluid domain boundary is discretized by a collection of quadric panels. The unknown quantities, including the free surface elevation, the normal flux over the free surface and the potential on the fluid domain boundary, are determined at each time step. The numerical results are compared with experimental data and other numerical solutions, showing satisfactory agreements.

Time domain simulations of the wave-induced motions of ships in maneuvering condition

The wave-induced motions of ships in maneuvering condition are numerically studied based on potential theory. The total disturbance potential is decomposed into a basic part and a perturbation part. The basic flow is evaluated based on the double-body model with a trailing vortex sheet. The perturbation flow is solved by using a time domain Rankine panel method to determine the hydrodynamic forces, and the wave-induced ship motions are then evaluated by an Adam–Moulton scheme. The solving process of the wave-induced motion is integrated with the maneuvering prediction by using a two–time scale model. Numerical tests are firstly carried out for a Series 60 ship, and the numerical results are compared with the experimental data to validate the numerical method for the basic flow. Then the wave-induced motions of the S-175 container ship in straight course and in turning condition are simulated; the numerical results are compared with the ITTC data and the experimental data, which show fairly good agreements.

Rankine time-domain method with application to side-by-side gap flow modeling

The performance of a time domain Rankine panel method applied to the seakeeping problem of two ships in side-by-side configuration is investigated in this article. Benchmark data for the numerical results are provided by fundamental seakeeping tests carried out in the towing tank of the CEHINAV-Technical University of Madrid. The multi-body system was composed by a barge and a prismatic geosim, which were subjected to regular head waves in two different gap distances. The motions of the geosim model were restricted to surge, heave and pitch, whereas the barge model was kept fixed. This set-up was adopted so as to guarantee that the gap width remained constant during the tests, providing a favorable situation for the numerical modeling of the system. Comparison between measurements and numerical results illustrates the limitation of potential flow solvers concerning the modeling of this hydrodynamic problem. Numerical wave resonance in the gap led to wave elevations and body motions much larger than those observed during the tests. In addition, the time domain method also presented convergence problems for a range of frequencies associated to the gap resonance phenomenon. In order to overcome these problems, an external damping factor was introduced in the time domain simulations, bringing a significant improvement to the numerical convergence of the method. Moreover, despite the simplicity of the damping model adopted, the results showed that this technique was indeed able to improve the computational predictions, leading to a closer agreement between the experiments and the numerical results.

Numerical study on added resistance of ships by using a time-domain Rankine panel method

This paper considers the numerical computation of added resistance on ships. As a method of solution, a higher-order Rankine panel method is applied in time domain. Furthermore, two different formulations, Neumann–Kelvin and double-body linearizations, are applied to investigate the difference between computational results. The quantities of added resistance are obtained by integrating the second-order pressure on the body surface. Computational results are validated by comparing with experimental data and other computational results on several models, and fair agreements are found for all the models. The components of added resistance are observed with regard to integral terms, radiation and diffraction components. This study continues to the computation of added resistance in irregular waves. This kind of computational approach can provide some important information to understand the uncertainty level of towing-tank measurement of added resistance. In this study, a series of long numerical simulations are carried out, and their statistical variations are observed for different time windows. Based on this observation, an appropriate criterion and averaging method are proposed for the prediction of added resistance in irregular waves.

Time-domain analysis of nonlinear motion responses and structural loads on ships and offshore structures: development of WISH programs

The present paper introduced a computer program, called WISH, which is based on a time-domain Rankine panel method. The WISH has been developed for practical use to predict the linear and nonlinear ship motion and structural loads in waves. The WISH adopts three different levels of seakeeping analysis: linear, weakly-nonlinear and weak-scatterer approaches. Later, WISH-FLEX has been developed to consider hydroelasticity effects on hull-girder structure. This program can solve the springing and whipping problems by coupling between the hydrodynamic and structural problems. More recently this development has been continued to more diverse problems, including the motion responses of multiple adjacent bodies, the effects of seakeeping in ship maneuvering, and the floating-body motion in finite-depth domain with varying bathymetry. This paper introduces a brief theoretical and numerical background of the WISH package, and some validation results. Also several applications to real ships and offshore structures are shown.

Time-domain analysis of nonlinear motion responses and structural loads on ships and offshore structures: development of WISH programs

The present paper introduced a computer program, called WISH, which is based on a time-domain Rankine panel method. The WISH has been developed for practical use to predict the linear and nonlinear ship motion and structural loads in waves. The WISH adopts three different levels of seakeeping analysis: linear, weakly-nonlinear and weak-scatterer approaches. Later, WISH-FLEX has been developed to consider hydroelasticity effects on hull-girder structure. This program can solve the springing and whipping problems by coupling between the hydrodynamic and structural problems. More recently this development has been continued to more diverse problems, including the motion responses of multiple adjacent bodies, the effects of seakeeping in ship maneuvering, and the floating-body motion in finite-depth domain with varying bathymetry. This paper introduces a brief theoretical and numerical background of the WISH package, and some validation results. Also several applications to real ships and offshore structures are shown.

Vlasov 보 모델을 이용한 컨테이너 선박의 스프링잉 응답해석

Modern ultra-large container carriers can be exposed to the unprecedented springing excitation from ocean waves due to their relatively low torsional rigidity. Large deck opening on the deck of container carriers tends to cause warping distortion of hull structure under wave-induced excitation, eventually leading to the higher chance of resonance vibration between its torsional response and incoming waves. To handle this problem, a higher-order B-spline Rankine panel method and Vlasov-beam FE model was directly coupled in the time domain, and the coupled equation was solved by using an implicit iterative method. In order to capture the complicated behavior of thin-walled open section girder, a sophisticated beam-based finite element model was developed, which takes into account warping distortion and shear-on-wall effect. Then, the developed beam model was directly coupled with the time-domain Rankine panel method for hydrodynamic problem by using the fixed-point iteration method. The developed computational scheme was validated through the comparison with the frequency-domain solution on the container carrier model in linear springing regime.

Time domain springing analysis on a floating barge under oblique wave

This paper studies the springing response of a flexible floating barge under an oblique wave. A time domain Rankine panel method was used to represent fluid motion surrounding a flexible seagoing vessel, and a finite element method was used for structural response. For accurate prediction of the structural response under an oblique wave, special attention was given to the structural model, such as the effect of warping distortion and bending-torsion coupling. The Vlasov assumption was followed for a deformable beam element to take into account the effect of warping distortion so that the cross section of the beam deforms out of its original plane without changing its cross-section contour. The coupled equation for both the fluid and structural domain was solved by using the implicit iterative method. A fixed point iteration with a relaxation scheme was employed in this study with the aid of the Aitken δ2 process seeking acceleration of solution convergence. Accuracy of a developed computer program was verified through the comparison with experimental work done by Remy et al. (Experimental and numerical study of the wave response of a flexible barge, Hydroelasticity in Marine Technology, Wuxi, 2006) resulting in good correspondence between the two results.

Ship Seakeeping Through the t = 1/4 Critical Frequency

This study demonstrates that a bounded, physically relevant solution does exist at the so-called T = Uω/g = 1/4 resonance in the linear seakeeping problem for a realistic ship with forward speed, U, frequency of encounter, ω, and gravitational acceleration, g. The solution of the seakeeping problem by a linear, three dimensional, time-domain Rankine panel method, validated through numerical analysis, testing, and comparison to physical experiments, supports this claim. The solution can also be obtained with equal validity through frequencies both above and below the critical frequency.