Wave Drift Forces Research Articles

An application of dynamic positioning control using wave feed forward

AbstractThe paper presents the results of model tests for a large tanker in which wave drift force feed forward was applied in the dynamic positioning control system. The estimation method of the nonlinear (second order) wave drift forces from the measurement of relative water motions at the side of a ship hull is presented. The estimated wave drift forces are used in the DP control system, to enhance the filter process of the extended Kalman filter, and in the required thruster set‐points. The EKF uses the nonlinear equations of low‐frequency ship motions on the horizontal plane, which are also presented.The results of the model tests show that the use of wave drift force feed forward significantly improves the positioning accuracy in sea states with 3.5 m significant wave height or higher. Copyright © 2001 John Wiley & Sons, Ltd.

Nonlinear dynamics and stability of spread mooring with riser

The dynamics of a floating vessel with its spread mooring and riser subjected to environmental excitation from current, wind, and waves is studied to investigate the effect of riser dynamics on the stability and bifurcation sequences of stationkeeping. A design methodology is developed to reveal the dependence of slow motion dynamics of spread mooring systems (SMS) on several design parameters, such as riser location, water depth, length and fairlead of mooring lines, orientation and pretension in the mooring lines. Nonlinear stability and bifurcation theory are used to produce catastrophe sets in the design space defining regions of qualitatively different dynamics. Limited time simulations are performed to verify the richness of the non-linear system dynamics identified in the catastrophe sets. The mathematical model is based on the third-order maneuvering equations in the horizontal plane including hydrodynamic memory. The riser dynamics is modeled quasi-statically by a nonlinear three-dimensional large deformation finite element model. Mooring lines are modeled by deep-water catenaries with drag and touchdown effect. External excitation consists of time-independent current, wind, and mean wave drift forces.

On the drifting speed of floating bodies in waves

In this paper, wave drifting speed of a floating body is discussed.Measurements of wave drifting speed were conducted on both two-dimensional floating body and three-dimensional floating body. Then, the theoretical calculation method of wave drifting speed was derived from the analyses of measurement results.The mechanism of wave drifting speed varies with wavelength. In the range of short wavelength, wave drift force due to reflection waves drifts the floating body; therefore the drifting speed is decided by the equilibrium of wave drift force and fluid drag, and it is proportional to the wave sloop. In the range of long wavelength, on the other hand, wave drift force hardly acts on the floating body, because wave almost transmits the floating body; therefore the drifting speed is decided by the wave-current speed and it is proportional to the square of the wave sloop. Taking these wave drifting mechanisms into consideration, an estimation method of wave drifting speed, which covers entire wave range, is proposed.

An Aid to Operating Decisions Based on Nonlinear Response of a Crane Barge in Waves

A nine-degree-of-freedom time domain mathematical model was used to numerically simulate crane ship dynamics. This model considers the elasticity and damping of the hoisting rope assembly and includes arbitrary, biangular swing of the suspended hook load coupled with surge, sway, heave, roll, pitch, and yaw motions of the hull. The linear frequency-dependent hydrodynamic response to the hull’s own motions accounted for memory effects that were approximated in the time domain by a finite state space model. The nonlinear hydrodynamic drag force acting on the oscillating hull was quadratically approximated using an empirical drag coefficient. The incident wave force on the hull consisted of the first-order force oscillating at wave frequency and the second-order slowly varying wave drift force. The nonlinear horizontal mooring system restoring force was approximated by a third-order polynomial. To specify operating limits for a shear-leg crane barge in a heavy lift offshore operation, a stochastic analysis was performed based on the system’s simulated dynamic response in an ensemble of natural seaways.

Wave-drift damping in slow surge–sway–yaw coupling motions of a cylinder array

Both experimental and theoretical investigations were made on wave-drift damping of a moored array of circular cylinders which undergo slow oscillations in horizontal modes, i.e., surge, sway, and yaw, due to the nonlinear excitation of ocean waves. Detail descriptions of the experimental arrangement and methods of processing the measured data are given. The model is restrained from the linear responses to wave excitations. An assumption of a quasisteady state for each position of rotation is made in data processing for the yaw mode of slow motion. To calculate wave-drift damping, the slow oscillations are approximated by the corresponding steady motions. The velocity potential is expanded into perturbation series based on two small parameters that measure wave slope and the velocity of steady flow, respectively. Wave-drift forces (moment) are calculated by the far-field method. Some new treatments to deal with the integral over the free surface are presented to improve the convergence and accuracy. The results of calculations and experiments are compared and satisfactory agreement is observed, which verifies the theory.

On Steady Drifting Motion of a Ship in Waves

Experiment is carried out to measure hydrodynamic forces and moment in oblique motion in calm water for a training ship model. Wave drift forces and moment for various wavelength and encounter angle for the ship in drifting motion is estimated by calculation of 3-D panel method based on an assumption that these can be approximated at zero forward speed. Equations of motion of steady drifting condition in long crested regular wave are solved by using experimental and calculated hydrodynamic forces and moment. Plural solutions obtained shows that steady drifting condition is not unique.

Time-domain analyses of elastic response and second-order mooring force on a very large floating structure in irregular waves

Real sea areas where very large floating structures are installed are random wave fields. Then, it is necessary to analyze the responses in the time domain due to directional waves. There exist hydroelastic deflections and slow drift motions in the responses of VLFSs in ocean waves. However, it is very time consuming to solve the equations of motion in the time domain and obtain these responses due to directional waves. It is unnecessary to solve such equations in the time domain, if mooring forces can be turned into on equivalent linear system. In this paper, we analyze the time-series responses without solving the equations of motion in the time domain. And, the corresponding model tests in uni- and two-directional irregular waves are carried out. The present method is validated by comparisons between the analytical and measured results of time histories, and moreover, the analytical method of a slowly varying wave drift force is also validated.

EFFECTS OF A SEA FLOOR STEP ON WAVE DRIFT FORCE

A linear and a fully nonlinear numerical wave tanks (NWTs) were applied to study wave drift force acts on a two-dimensional Lewis form body in finite depth wave flume. These NWTs are based on potential theory and the fluid and floating body motions are directly simulated in time domain. Boundary value problems both on the velocity potential φ and its time derivative ∂φ/∂t are solved at each time step. The coupling condition between fluid and floating body is imposed as the implicit boundary condition of ∂φ/∂t on wetted body surface. The radiation condition at both tank ends are satisfied by artificial damping technique. Using these NWTs, effects of the floor step of the flume on wave drift force were studied. Measurement of wave drift force was also conducted in our two dimensional wave flume. In this report, the results of simulations and measurements are presented and the effect of the floor step on wave drift force is discussed.

A STUDY ON MOTIONS AND DRIFT FORCES OF A MULTIBODY FLOATING SYSTEM IN WAVES

by Yoshiyuki Inoue *, Member, M. Rafiqul Islam * M. Murai *, MemberSummary In this paper, the application of three dimensional source technique for computations of motion responses and drift forces for multi-body floating system with zero forward speed in waves are investigated. The mean wave drift forces are obtained by far field and near field (direct pressure integration) methods. Numerical results for the first order motion responses and the mean wavedrift forces for a parallel arrangement of a FPSO (Floating Production Storage and Offloading Unit) and a LNG carrier are discussed. Some comparisons are made for a single floating body (semi-submersible) as well as for a simple multi-body system of a cylindrical body with a box shaped hull. Numerical results for motion responses are compared with experimental ones for the FPSO-LNG system and also results for mean wave drift forces obtained from both of the methods are compared with experimental ones. The trend of the results as well as correlation between both of the methods found to be comparatively well in agreement. The effects of roll damping to the second order wave drift forces for sway and yaw are also discussed.

Estimation method of slowly varying wave drift force acting on very large floating structures

It is necessary to estimate slowly varying drift forces on very large floating structures (VLFS) for their safety. The aim of our research is to develop an estimation method of such forces on VLFS in the real seas, i.e. in multidirectional irregular waves. We knew such a method for rigid bodies, but it seems to be complicated to extend the method for VLFS directly because of their hydroelastic behavior. Thus, in the previous report, we presented an easy but legitimate estimation method in which we can evaluate slowly varying drift forces by means of the integration of the squared relative wave height and also we validated our method with model tests in long crested irregular waves. In this 2nd report, we carried out a numerical calculation with various flexural rigidities of VLFS, incident angles, and incident wave periods to validate our method more generally. We also validated our method with model tests in short crested irregular waves so that we can demonstrate our method can be applied for VLFS in multidirectional irregular waves.

Estimation method of slowly varying wave drift force acting on very large floating structures

It is necessary to estimate slowly varying drift forces on very large floating structures (VLFS) for their safety. The aim of our research is to develop an estimation method of such forces on VLFS in the real seas, i.e. in multidirectional irregular waves. We knew such a method for rigid bodies, but it seems to be complicated to extend the method for VLFS directly because of their hydroelastic behavior. Thus, in the previous report, we presented an easy but legitimate estimation method in which we can evaluate slowly varying drift forces by means of the integration of the squared relative wave height and also we validated our method with model tests in long crested irregular waves. In this 2nd report, we carried out a numerical calculation with various flexural rigidities of VLFS, incident angles, and incident wave periods to validate our method more generally. We also validated our method with model tests in short crested irregular waves so that we can demonstrate our method can be applied for VLFS in multidirectional irregular waves.

A Real-Time Ship Manoeuvring Simulation Study for the Strait of Istanbul (Bosporus)

During the past thirty years, there has been a steady growth in the size and number of ships that use the Strait of Istanbul (Bosporus), which is one of the most difficult, crowded, and potentially dangerous waterways in the world. There have been over two hundred accidents over the past decade resulting in loss of life and serious damage to the environment. Many of the proposed export routes for forthcoming production from the Caspian sea region pass westwards through the Black Sea and the Bosporus en-route to the Mediterranean Sea and world markets. The risks and dangers associated with tanker navigation, maritime accidents and environmental catastrophe are aggravated with the increase in the density of traffic, tanker size and cargo capacity, as well as the nature of the cargo. In order to ease the problem, a Traffic Separation Scheme (TSS) was established and approved by IMO in 1994. This scheme has drastically reduced the number of collisions. However, one-way or two-way suspension of traffic in the Bosporus is inevitable for ships that cannot comply with the TSS because of their type, size or poor manoeuvring characteristics. The selection of size criteria to comply with the TSS has been a matter of discussion. This paper presents the results of a real-time simulation study investigating the manoeuvring performance of large tankers in the Bosporus. The study was conducted with a simulator capable of subjecting a given hull form to any combination of environmental conditions, i.e. wind, current and wave drift forces. The results indicate that, when realistic environmental conditions are taken into account, the size of ships that can navigate safely in compliance with the traffic separation lanes is limited.

Effect of Memory on the Stability of Spread Mooring Systems

The importance of including the hydrodynamic memory effect in modeling and analysis of spread mooring systems (SMS) is assessed based on the design methodology for mooring systems developed at the University of Michigan. The memory effect is modeled by the hydrodynamic radiation forces expressed in terms of added mass at infinite frequency and convolution integrals of impulse response functions. The convolution integrals, which are explicit functions of time, are converted to autonomous excitation by the method of extended dynamics. For a given SMS configuration, nonlinear stability and bifurcation theory are used to produce catastrophe sets in the parametric design space separating regions of qualitatively different system dynamics. This approach reveals the complete picture of nonlinear phenomena associated with system dynamics and eliminates the need for extensive simulations. Catastrophe sets are developed in several parametric design spaces, providing fundamental understanding of the memory effects on SMS nonlinear dynamics. The mathematical model is based on the slow-motion maneuvering equations in the horizontal plane, including hydrodynamic memory effect and third-order quasi-steady hydrodynamic forces. Mooring lines are modeled by synthetic fiber ropes attached to surface terminals and deep-water catenary chains with touchdown and nonlinear drag. Environmental loads consist of time-independent current, wind, and mean wave drift forces.

Estimation method of slowly varying wave drift force acting on very large floating structures

Estimation method of slowly varying wave drift force acting on very large floating structures

Estimation Method of Slowly Varying Drift Motion and Elastic Behavior of Pontoon Type Very Large Floating Body in Irregular Waves

A real elastic motion of a very large floating structure is complicated because a field that a VLFS will be installed is random sea area. Then, it is important to predict horizontal motions too, because slowly varying drift motion may occur in irregular waves. So, the motion responses must be investigated in irregular waves.In this paper, one method in order to calculate a time series of wave drift forces is shown. The validity of that method and the estimation method of wave drift forces is confirmed by comparing with the corresponding experimental results. Then, the time histories of vertical and horizontal displacements are compared. And, this paper proposes the some examinations on the estimation method of the wave drift force. They are the effect of an interaction among directional angles of incident waves and the necessary term in order to predict it.

Low-frequency second-order wave-drift forces and damping

The effects of free-surface waves on floating structures is of great importance in the offshore industry. Besides the first-order responses to the waves, second-order effects play a role, in particular, in the situation where an anchored object may be excited in its frequency of resonance. This paper concerns the study of this phenomenon. Two different approaches are developed, each with its own advantage. Special attention is paid to excitation forces generating the motions; also a theory to determine the inviscid damping that limits the extreme excursions is treated. Numerical results are presented for a sphere, while numerical results for two classes of tankers, namely for a VLCC and a LNG-carrier, and a semi-submersible are compared with experimental data obtained at the Maritime Research Institute in the Netherlands (MARIN).

Nonlinear Control of Underactuated Ships with Forward Speed Compensation

In this paper a nonlinear control law for an underactuated ship is derived by using a nonlinear ship model which includes the hydrodynamic effects due to time-varying speed and wave frequency. The nonlinear ship model does not have the structural properties of symmetric inertia and positive damping at high speed, which have been a common assumption when designing nonlinear ship tracking control systems. Backstepping control designs are used to circumvent the problem of a non-symmetrical inertia matrix. In this paper we have considered a ship with one propeller and one bow thruster. This is actually an underactuated system since only two actuators are used to control three degrees of freedom. The application of speed and wave dependent models for ship control is a first step towards the design of a new generation of nonlinear ship control systems that can operate under time-varying speed and wave frequency conditions. Previous work has often relied on the assumption of constant speed, and practical solutions have been based on switching between different control schemes at different speeds. Compensation of slowly-varying environmental disturbances, such as ocean currents, 2nd-order wave drift and wind forces are done by using adaptive backstepping. For tracking applications, global convergence is proven by using Barbalat's lemma. Computer simulations illustrate the performance of the control law.

Hydroelastic Responses of Pontoon Type Very Large Offshore Structure

The authors consider a pontoon type flexible floating airport as the very large floating structure. In order to design this kind of structure, we have to investigate several key points in advance. Among those key points, estimation of the wave drift forces is very important in order to design of the mooring system. In this paper, the authors consider the square type flexible flat plate with shallow draft, exactly speaking, zero draft as the floating airport. The authors develop the computer code of the slowly varying wave drift force for an elastic floating structure with shallow draft based on the so called Near Field Method which is validated by both the Far Field Method and the corresponding Experiments.The authors conclude that even though the water depth is shallower, there is no big difference among the steady wave drift forces in each water depth, while the rigidity of the structure is smaller, more flexible, then, the steady wave drift forces or mooring forces are smaller.Finally, they showed the flexibility of a floating structure decreases not only steady wave drift forces but also slowly varying wave drift forces under the numerical time domain simulation of a very large floating structure with the multiple dolphins mooring system.

The hydrodynamic forces acting on a cylinder array oscillating in waves and current

The problem of the interaction of multiple cylinders oscillating in waves and slow current is considered. The interaction is represented by waves emitted from adjacent cylinders towards the cylinder under consideration. Wave drift forces and moment in the horizontal plane are calculated by the far-field method based on the conservation of momentum or angular momentum. A semianalytical formula for the calculation of the wave drift damping is then deduced. The conservation of the integrals in these formulae is proved. Special treatments to improve the accuracy of results are discussed. Comparisons between calculated results and experimental measurements are made, showing satisfactory agreement. Effects of various combinations of current direction and incident wave angle on the wave drift damping and damping moment are also examined.

Mooring System Design Based on Analytical Expressions of Catastrophes of Slow-Motion Dynamics

Analytical expressions of the necessary and sufficient conditions for stability of mooring systems representing bifurcation boundaries, and expressions defining the morphogeneses occurring across boundaries are presented. These expressions provide means for evaluating the stability of a mooring system around an equilibrium position and constructing catastrophe sets in any parametric design space. These expressions allow the designer to select appropriate values for the mooring parameters without resorting to trial and error. A number of realistic applications are provided for barge and tanker mooring systems which exhibit qualitatively different nonlinear dynamics. The mathematical model consists of the nonlinear, third-order maneuvering equations of the horizontal plane slow-motion dynamics of a vessel moored to one or more terminals. Mooring lines are modeled by synthetic nylon ropes, chains, or steel cables. External excitation consists of time-independent current, wind, and mean wave drift forces. The analytical expressions presented in this paper apply to nylon ropes and current excitation. Expressions for other combinations of lines and excitation can be derived.