Equations Of Ship Motions Research Articles

Data-driven system identification of hydrodynamic maneuvering coefficients from free-running tests

A data-driven system identification approach was developed to identify the hydrodynamic coefficients of a mathematical maneuvering model. The method, developed primarily for use in the context of autonomous shipping, solved the ship motion equations using measurements from free-running model tests, whereby an efficient recently developed Euler equation-based numerical approach determined the zero-frequency added masses. The method is simple and robust and incorporates the physical properties of hydrodynamic forces to enforce a physically realistic solution. The method was verified and validated with free-running maneuver tests. The predicted ship kinematics and trajectories compared favorably with the measurements. The potential of the method was demonstrated.

Towards the effects of load condition on ship manoeuvrability by a system simulation method with hydrodynamic derivatives from RANS computations

The effects of load condition on ship manoeuvrability are investigated by means of system simulation method. To this end, a MMG-type mathematical manoeuvring model is applied to simulate the standard turning and zigzag rudder manoeuvres for a KVLCC2 ship model in six load conditions (two drafts × three trims). In order to determine the needed hydrodynamic derivatives, the forces and moments on the hull in a range of combined static drift and circle motions are computed by using the own expanded RANS (Reynolds-Averaged Navier-Stokes) solver on OpenFOAM. However, the coefficients of hydrodynamic interaction among hull, propeller and rudder are obtained from available experiments. The computed surge forces, sway forces and yaw moments agree fairly well with the experimental data, suggesting a promising prospect for the used RANS solver in the application of ship manoeuvring prediction. By regressing the hydrodynamic forces and moments, the hydrodynamic derivatives are obtained. Turning and zigzag rudder manoeuvres are simulated by solving ship motion equations in line with the acquired derivatives and coefficients. Comparing the simulated results between the full and ballast load condition without trim, a small draft (i.e. the ballast load condition) improves turning performance, but weaken course stability. For the three full load conditions or ballast load conditions, trim by bow improves turning ability, but deteriorates yaw-checking ability. The simulated results for two load conditions show satisfactory agreement with available experimental data, which suggests that the present procedure for ship manoeuvring prediction is effective. The course stability indexes are analysed as well. The load condition will affect significantly the manoeuvrability of a ship, at least for KVLCC2. It may be quite necessary to evaluate the manoeuvrability of a ship in different load conditions at the initial design stage.

Investigation on time-domain simulation and experiment of harmonic rolling of ultra-large container ship in waves

When an accident due to harmonic rolling occurs, loss will be huge, especially for ultra-large container ships (ULCS). In the paper, the time-domain method is adopted to study and analyze the occurrence of non-linear harmonic rolling phenomenon of ULCS and subsequent motion behaviors. Under the weakly scattering hypothesis, six-degree-of freedom(6-DOF) time-domain ship motion equation is established by employing impulse response function. The incidental wave force and the restoring force are obtained by pressure integrating on instantaneous wet surface, while the roll damping coefficient is obtained by experiment. An ULCS navigating in regular waves of various frequencies is numerically simulated and investigated by model tests. The characteristics and mechanism of harmonic rolling of the ship with different metacenter-heights, which sails in head and following waves of different periods, are studied and analyzed. The result comparison shows that the time-domain method used in the paper can predict the occurrence and motion amplitude of the harmonic rolling very well. Although the seaworthiness of ULCS is generally better than smaller ships, there is still the possibility of triggering the problem of harmonic rolling in real sea navigation. Thus, it is necessary to study and analyze during ship design.

Modeling the motion of large vessels due to tsunami-induced currents

This paper describes a model developed to predict the general behavior of large vessels under energetic tsunami conditions using established regional-scale tsunami models. The methodology is based on a two-way coupled approach to account for the interaction between vessels and flow, which becomes increasingly important in restricted waters. A shallow water hydrodynamic solver is modified to include vessels as horizontal pressure distributions, and friction coefficients are adjusted accordingly at the locations of vessels to account for the effects of skin friction. Adequacy of these modifications are then tested against a benchmark case designed in OpenFOAM®, and comparisons demonstrate the modified shallow water solver's ability to provide a reasonable realization for energetic flow passing a floating object. A vessel transport model coupled with the hydrodynamic solver is based on the linear equations of ship motion with three degrees of freedom (surge, sway and the yaw). Finally, the model is equipped with a collision solver founded on the concept of the conservation of momentum and impulse. Results from two large scale applications of the developed tool are presented. These analyses revealed that the flow in and around the ports is indeed strongly affected by the presence of vessels. Also, it is observed that the model can approximate the ship's behavior, but at the same time the model results are very sensitive to the initial choice of the input parameters due to the chaotic nature of the process.

Pure low-frequency and pure high-frequency ship motion equations in regular waves

The problem of ship motions in waves can be seen as a coupled problem of manoeuvring and seakeeping. The former is a low-frequency motion problem in terms of time scale of ship motion, whereas the latter is relatively a high-frequency motion problem. They can be separately predicted by solving a group of low-frequency ship motion equations and a group of high-frequency ship motion equations. However, the theoretical basis behind both usual groups of motion equations may be questionable. In our previous study, a time-averaged method was introduced to derive the pure low-frequency ship motion equations in regular waves. The new equations have a few additional terms which are the mean inertial forces and moments due to wave-induced high-frequency motions, compared with the usual equations. The low-frequency ship motion equations were then solved to predict ship manoeuvring in waves by means of a modelling approach. It has been demonstrated that these additional terms are non-negligible for manoeuvring prediction, if amplitudes of high-frequency motions are large enough, e.g. in the condition of long wave length and large wave amplitude. In this study, we will give out the more complete pure low-frequency ship motion equations in regular waves and some new explanations. The pure high-frequency ship motion equations are also derived by subtracting the pure low-frequency ship motion equations from transient ship motion equations. On the aspect of manoeuvring prediction, there are two improvements, as compared with before. One is that the mean inertial forces and moments due to second-order high-frequency motions are retained in the pure low-frequency motion equations. The other is that the effect of longitudinal ship speed is taken into account in the modelling approach. As will be shown, the prediction accuracy is improved.

A Time-Averaged Method for Ship Maneuvering Prediction in Waves

The concept of time-averaged motion is introduced to analyze the coupled ship maneuvering and seakeeping problem. Based on this concept, new equations of ship motion, referred to as time-averaged equations, are proposed for ship maneuvering prediction in waves. The present work is to describe and verify the new method. For the latter, the maneuverability of container ship S-175 in regular waves is predicted by solving the equations, where forces and wave-induced high-frequency motions are approximated by means of a modeling approach. The results are compared with available experimental data. It is indicated that the new method is very promising because satisfactory agreements are found between predictions and experiments. In addition, the influences of wave-induced high-frequency motions on maneuverability are analyzed and discussed.

Mechanism of dynamic automatic collision avoidance and the optimal route in multi-ship encounter situations

Autonomous navigation on the open sea involving automatic collision avoidance and route planning helps to ensure navigational safety. To judge whether all target ships (TSs) will pass safely and find the optimal route under multi-ship encounter situations, the relationship between the variations in the own ship (OS) velocity vector after nonlinear course altering motion and the collision avoidance result, which is defined as the collision avoidance mechanism, was analyzed. Methods producing the optimal route were also proposed. First, the static collision avoidance mechanism based on the ship domain and velocity obstacle (VO) was introduced. On that basis, the collision-free course alteration range of the OS, without consideration of the real manoeuvring process, was presented. Second, the ship motion equations and fuzzy adaptive proportion integral derivative (PID) control method were combined to develop a course control system. This system was then used to predict OS motions during the course-altering process. Based on this prediction, TS positions were calculated. Subsequently, the dynamic collision-free course altering ranges for the OS were obtained. Third, a model to compute the optimal route was introduced. Finally, simulations were performed under a situation including six TSs and two static objects, and the shortest collision-free route that satisfies both regulations for preventing collisions and good seamanship was found.

Time-domain hydroelastic analysis of nonlinear motions and loads on a large bow-flare ship advancing in high irregular seas

This paper investigates the nonlinear hydroelastic motion and load responses on a large flexible ship advancing in harsh irregular waves. A 3D time-domain nonlinear hydroelasticity theory for the prediction of ship motions, deformations and wave loads in long-crested irregular waves is presented. The nonlinear Froude–Krylov force and hydrostatic restoring force are calculated on the instantaneous wetted hull surface while the linear diffraction force and radiation force are estimated on the static mean wetted surface. The radiation forces are estimated by retardation function method to take account of the wave memory effects and forward speed effects. The slamming loads that were derived by momentum impact theory are also included in the ship motion equation to investigate the whipping responses. The hydrodynamic and structural responses are fully coupled by modal superposition principle to consider the hydroelastic effects including springing and whipping responses. The numerical results are well validated by the experimental data of a segmented model with large flare-bow tested in an ultra-long laboratory tank. The numerical and experimental data of ship responses in different irregular wave conditions are systemically analyzed and compared by time series analysis, spectral analysis, and probability statistics analysis methods.

Structure and Parameter Identification of Ship's Multi-motion State Model

ABSTRACT Bai, J.; Mao, Z., and Pu, T., 2018. Structure and parameter identification of ship's multi-motion state model. In: Liu, Z.L. and Mi, C. (eds.), Advances in Sustainable Port and Ocean Engineering. Journal of Coastal Research, Special Issue No. 83, pp. 892–896. Coconut Creek (Florida), ISSN 0749-0208. At present, the problem of poor accuracy of parameter identification exists in the method of ship's multi-motion model structure and parameter identification based on operational modal analysis. Therefore, this paper presents a structure and parameter identification method of ship's multi-motion model based on extended Calman filter. In this method, the ship motion equation is established in the fixed coordinate system, and to convert to the computation of motion variables, to obtain the ship motion state model, and realize the identification of ship motion state parameters by using the augmented state equation and extended Calman filter. The experimental results show that the Zig-zag experiment value...

A new URANS based approach on the prediction of vertical motions of a surface combatant in head waves

In this study, wave excitation and radiation terms in 2DOF equations of vertical ship motion are obtained by using a URANS solver based on the finite volume method. The DTMB 5512 hull form is chosen for the calculations at the Froude number of 0.41. Numerical simulations are performed for 7 different regular wave conditions. First, in the regular wave, the excitation heave force and pitch moment with the related phase angle are computed while the ship is fixed to heave and pitch motions. Then, the body is forced to oscillate in the heave and pitch directions with a certain frequency and the radiation coefficients are obtained. After finding the excitation and radiated terms, the 2DOF vertical ship motion equations are solved in the frequency domain, and motion transfer functions are plotted. The results are compared with those obtained through strip theory, fully nonlinear URANS approach and experiments. The new URANS based approach presented in this paper offers a more accurate prediction of vertical ship motions compared to strip theory outputs because it takes the viscous effects and free surface nonlinearities into account. The new URANS based approach can be considered as a better alternative to the fully nonlinear URANS approach.

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.

Navigation Condition Effect on Ship Motion in some Sea State

According to analyzing the identity of ocean wave, theory of wave energy spectrum was applied to compute the curve of wave elevation vs. time in some sea state. Based on ship motion equations, ship motion was acquired by the simulation software of the of ship strip theory in some situation. How different navigation conditions effect on ship motion is researched in some sea state. The results show the change of degree of abaft the beam badly influenced the amplitude and periods of pitch, it also influenced periods of heave and amplitude of roll. The change of ship speed influenced the amplitude and periods of pitch, it also influenced periods of heave and roll.

The Conception and Mechanism of Ship Frequency Scattering due to Maneuvering Motions in Regular Waves

By adopting ship motion equation of rolling with single-freedom degree, together with coupled heave-pitch motion equation, the irregular oscillatory motion of maneuverability response in regular waves was numerically simulated in this paper. Based on the presupposition of harmonic wave encounter frequency, the concept of frequency scattering of wave encounter frequency was presented. The constant value, as well as intensity and frequency, of wave frequency of encounter were defined, and the dispersion relation of wave encounter frequency was deduced also. Furthermore, two kinds of mechanism for the frequency scattering resulted from the change of speed and wave angle respectively, were obtained.

Problem of water flow on deck

A ship moving in waves is exposed to various undesired phenomena. Among them is water trapped on deck that affects ship safety. This paper presents a numerical model, based on shallow water flow, describing water flow on deck. Simplified methods have been applied to determine forces due to the water on deck influencing ship motion in waves. The presented method is developed to be included in the ship motion equation.

On unstable ship motions resulting from strong non-linear coupling

In this paper, the modelling of strong parametric resonance in head seas is investigated. Non-linear equations of ship motions in waves describing the couplings between heave, roll and pitch are contemplated. A third-order mathematical model is introduced, aimed at describing strong parametric excitation associated with cyclic changes of the ship restoring characteristics. A derivative model is employed to describe the coupled restoring actions up to third order. Non-linear coupling coefficients are analytically derived in terms of hull form characteristics. The main theoretical aspects of the new model are discussed. Numerical simulations obtained from the derived third-order non-linear mathematical model are compared to experimental results, corresponding to excessive motions of the model of a transom stern fishing vessel in head seas. It is shown that this enhanced model gives very realistic results and a much better comparison with the experiments than a second-order model.

A Non-Linear Mathematical Model of Higher Order for Strong Parametric Resonance of the Roll Motion of Ships in Waves

Non-linear equations of ship motions in waves describing the couplings between heave, roll and pitch are investigated. A third order mathematical model is introduced, aimed at describing strong parametric excitation associated with cyclic changes in the ship restoring characteristics. A derivative model is employed to describe the coupled restoring actions up to third order. Non-linear coupling coefficients are derived in terms of hull form characteristics. In the present investigation, experimental results corresponding to excessive motions of a transom stern fishing vessel in head seas are compared to numerical simulations obtained from the derived third order non-linear mathematical model. It is shown that this enhanced model gives good results and a better comparison with the experiments than a second order model.

3-D computational method of wave loads on turret moored FPSO tankers

A three-dimensional method of calculating wave loads of turret moored FPSO (Floating Production Storage and Offloading) tankers is presented. The linearized restoring forces acting on the ship hull by the mooring system are calculated according to the catenary theory, which are expressed as the function of linear stiffness coefficients and the displacements of the upper ends of mooring chains. The hydrodynamic coefficients of the ship are calculated by the three-dimensional potential flow theory of the linear hydrodynamic problem for ships with a low forward speed. The equations of ship motions are established with the effect of the restoring forces from the mooring system included as linear stiffness coefficients. The equations of motions are solved in frequency domain, and the responses of wave-induced motions and loads on the ship can be obtained. A computer program based on this method has been developed, and some calculation examples are illustrated. Analysis results show that the method can give satisfying prediction of wave loads.

AN EXACT SOLUTION FOR A SIMPLIFIED MODEL OF THE HEAVE AND PITCH MOTIONS OF A SHIP HULL DUE TO A MOVING LOAD AND A COMPARISON WITH SOME EXPERIMENTAL RESULTS

The coupled heave and pitch motions of a simplified non-uniform ship hull floating on a still water surface and subjected to a moving load have been investigated. The ship hull was considered to be a rigid body supported by an elastic foundation with distributed springs and dampers. Based on the general equations of ship motions in waves, the governing equations of the ship hull were derived. For the case of a constant moving load speed, a closed form “exact solution” was obtained. For the purpose of comparison and more general studies, a numerical approach was also introduced. The influences on the dynamic responses of ship hull of some factors such as the moving load speed, direction of movement, landing position, initial velocity and acceleration, were studied. To check the reliability of the numerical results, a simple model test was conducted and approximate agreement was obtained. The reasons for the discrepancies between the experiments and theory are discussed. For simplicity, the damping effects due to ship-motion-induced waves are replaced by the damping ratios in this study.

Forward speed effects in the equations of ship motion

The explicit speed dependency of the coefficients in the linear equations of ship motion is determined from an energy formulation of the problem as opposed to the usual strip-theory formulation. For a completely symmetrical (longitudinal and lateral) ship, the cross-coupled damping coefficients resulting from the energy approach are shown to satisfy the Timman and Newman symmetry theorem identically. For ships possessing lateral symmetry only, a different form of symmetry among the cross-coupled damping coefficient is found to exist. The results of the energy approach are found to agree quite well with the results of three strip-theory formulations regarding the speed dependency of the coefficients in the heave and pitch equations.

Dynamical Theory of Potential Flows with a Free Surface: A Classical Approach to Strip Theory of Ship Motions

The application of the dynamical theory to problems involving a solid body moving in an unbounded medium of inviscid and incompressable fluid is well known in classical hydrodynamics. The distinctive feature of this method is that the fluid and the body together are treated as one dynamical system and the description of the problem requires only one single source of information, the kinetic energy of the fluid resulting from the motion of the solid body. In this paper, the application of this classical method to floating-body problems is presented. In particular, the method is applied to derive the dynamic coefficients in the equations of ship motion following the strip-theory approximation. Formulas for the added-mass and dampling coefficients are obtained, and the differences as compared with those used in the latest version of strip theory are discussed.