Study on 2nd-Order Wave Loads With Forward Speed Through Aranha’s Formula and Neumann-Kelvin Linearization

The 2nd-order wave loads consist of difference frequency, sum frequency components and a steady drift component that is also called the mean drift load. The first two components are usually not of interest, because of their small amplitudes compared with the 1st-order wave loads. The remaining mean drift load should be taken into consideration due to its steady effect on floating bodies. In the previous research, the full derivation and expression of the 2nd-order wave loads applied to a floating structure was presented. Moreover, numerically estimated quadratic transfer function was also illustrated with both off-diagonal elements and diagonal elements called the mean drift coefficients. Most research topics in this scenario consider the wave only case. In this paper, the mean drift wave loads applied to a floating structure with forward speed or current velocity has been numerically estimated through Aranha’s formula, a far field method and Neumann-Kelvin linearization, a near field method. Therefore, the effect of the floating structure’s forward speed or current velocity on the 2nd-order mean drift loads that is also called the wave drift damping has been discussed through these two methods. This work will provide a meaningful reference and numerical basis for the ongoing projects of the floating structure’s seakeeping and maneuvering problems.

A Framework of Numerically Evaluating a Maneuvering Vessel in Waves

Maneuvering in waves is a hydrodynamic phenomenon that involves both seakeeping and maneuvering problems. The environmental loads, such as waves, wind, and current, have a significant impact on a maneuvering vessel, which makes it more complex than maneuvering in calm water. Wave effects are perhaps the most important factor amongst these environmental loads. In this research, a framework has been developed that simultaneously incorporates the maneuvering and seakeeping aspects that includes the hydrodynamics effects corresponding to both. To numerically evaluate the second-order wave loads in the seakeeping problem, a derivation has been presented with a discussion and the Neumann-Kelvin linearization has been applied to consider the wave drift damping effect. The maneuvering evaluations of the KVLCC (KRISO Very Large Crude Carrier) and KCS (KRISO Container Ship) models in calm water and waves have been conducted and compared with the model tests. Through the comparison with the experimental results, this framework had been proven to provide a convincing numerical prediction of the horizontal motions for a maneuvering vessel in waves. The current framework can be extended and contribute to the IMO (International Maritime Organization) standards for determining the minimum propulsion power to maintain the maneuverability of vessels in adverse conditions.

Effects of Wave-Current Interaction on Floating Bodies

Wave-current interaction effects may significantly influence the mean wave drift forces on a structure as well as the motion responses and wave elevation around the structure. Additionally, the drift force may be used to estimate the wave drift damping of a moored structure. A new numerical potential theory code for industry applications (MULDIF) has been recently developed, where the hydrodynamic interaction between waves and current of arbitrary direction with large volume structures is consistently included. The code also handles multiple bodies and finite water depth including wave-current interaction effects. The aim has been to create a robust and easy-to-use practical tool. Initial validation studies against model tests have been conducted. The numerical results show a strong heave-pitch coupling due to the presence of the current. Preliminary results for a semi-submersible show good agreement for the motions provided that the mooring used in the model tests are accounted for. The free surface elevation around the semi-submersible is presented in contour plots.

A 3D Higher Order Time Domain Rankine Panel Method for Wave-Current Interaction

The wave-current effects are very important in several offshore applications, for instance, the wave-drift-damping of a Turret moored FPSO. This papers presents the incorporation of current effects in the higher order time domain Rankine Panel Method on development in the Numerical Offshore Tank (TPN) at the University of São Paulo (USP) already introduced in [1]. The method is based on a perturbation theory to study first and second order effects, considering the geometry described using NURBS (Non Uniform Rational Basis Spline) and the potential function, free surface elevation, pressure etc by B-splines of arbitrary degree. The study is performed for a simplified geometry (sphere) and the results regarding a fixed hemisphere compared to other numerical methods considering both first and second order quantities are presented.

First and Second Order Wave-Current Interactions for Floating Bodies

The influence of current in sea-keeping problems is felt not only for first order quantities such as wave run-ups in front of the structure, but also mainly for second order quantities. In particular, the wave drift damping (which is expressed as the derivative of drift force with respect to the current) is of special interest for mooring systems. The interaction effects of a double-body steady flow on wave diffraction-radiation is studied through a decomposition of the time-harmonic potential into linear and interaction components. A boundary integral method is used to solve the first order problem. Ultimately, a far-field method is proposed to get access to second order drift forces.

Current Effects on a Moored Floating Platform in a Sea State

The significance of current-induced forces and effects on a moored semisubmersible production platform in various sea state conditions is explored, with emphasis on surge motions. Experimental data from 1:55 scaled model tests in a 50m × 80m wave basin are investigated. A description of the current generation is given first. The current in the actual basin is modelled by use of a return current under a false bottom. The importance of modelling a “real” physical current for the proper reproduction of platform responses is pointed out. The semisubmersible tests are carried out with the platform in current only, in irregular waves only, and in combined waves and current conditions. The effects from the current on platform motions and mooring line tensions are investigated. Vortex-Induced motions (VIM) are observed in pure current, depending on the actual combination of current velocity and natural sway period. In combined waves and current the VIM seems to be more or less disappearing. A large effect is seen on the wave drift responses. Both drift forces, non-Gaussian properties and resulting extreme motions and line tensions are significantly increased, especially in high sea states. This is explained through a combination of wave drift damping and viscous effects. At the same time the damping is also increased, but this only partly compensates for the increased forces.

Effects of Wave Drift Forces on Maneuvering of Ship

The dynamic positioning system of floating ocean structures requires hydrodynamic force derivatives to construct an accurate maneuvering model. In a severe sea state, the effects of ambient wave field on the maneuvering properties are not negligible. To investigate wave drift forces affecting on maneuvering of a ship relating to dynamic positioning system, an innovative model test, i.e. the Planer Motion Mechanism (PMM) test in waves is discussed in the present paper. Meanwhile, a theory to evaluate wave drift force including wave drift damping and wave drift added mass is summarized. Some examples of experiments done in Ocean Engineering Wave Basin of Institute of Industrial Science, University of Tokyo are presented and compared with calculated results based on the above theory.

Numerical Prediction of MODUs Drift During Hurricane Katrina

During severe hurricanes, such as Katrina, the mooring system of a number of Mobile Offshore Drilling Units (MODUs) in the Gulf of Mexico failed. Drifting MODUs may potentially damage other critical elements of the offshore oil and gas infrastructure by colliding with floating or fixed production systems and transportation hubs, or by rupturing pipelines owing to their dragging anchors over the seabed. To avoid or mitigate the damage caused by a drifted MODU, it is desirable to understand the mechanics of the drift of a MODU under the impact of severe wind, wave and current and have the capability of predicting the trajectory of the drift. To explore the feasibility and accuracy of predicting the trajectory of a drifting MODU based on real-time or hindcast met-ocean conditions and limited knowledge of the condition of the drifting MODU, this study employed a simplified equation describing only the horizontal (surge, sway and yaw) motions of a MODU under the impact of steady wind, current and wave forces. The simplified hydrodynamic model neglects the first- and second-order oscillatory wave forces, unsteady wind forces (owing to wind gustiness), wave drift damping, and the effects of the body oscillation on the steady wind and current forces. It was assumed that the net effects of the oscillatory forces on the steady motion are insignificant. To verify the accuracy and feasibility of our simplified approach, the predicted drifts of two MODUs were compared with the corresponding measured trajectories recorded by the Global Positioning System (GPS).

Study of the Wave Drift Damping for a Very Large Crude Carrier

Pull-out test and decay tests in still water and in waves for the surge motion of a VLCC in ballast condition are carried out at LabOceano. The pull-out test associated with the mean drift displacement in regular waves is used to determine mean drift force. From the decay tests the damping coefficients are adjusted using the Froude energy method and the procedure based on the logarithm decrement. For the decay test in waves, the response is subdivided in the mean drift contribution, the regular wave response and the transient response. The wave drift damping is considered as an increase on the linear damping in still water. So, we introduce an additional damping to the linear part of the damping coefficient in still water and simulate the decay test in waves. Comparing the results from the simulation with the experiments the wave drift damping contribution is adjusted. Finally, the mean drift results are compared with the results obtained with the potential theory. The wave drift damping coefficients obtained from the experiments are compared with coefficients obtained with a formulation proposed in the literature.

Nonlinear Wave Loads Affected by the Low-Frequency Oscillations in the Horizontal Plane

To investigate the effects of the low-frequency oscillations on the nonlinear wave loads, the interaction of the low-frequency oscillations with the ambient wave fields is considered. The frequency of the slow oscillations is assumed to be much smaller than the wave frequency. Perturbation expansion based on two small parameters, i.e. the incident wave amplitude and the low frequency, is performed to simplify the problem. Nonlinear wave loads including the wave drift damping and wave drift added mass are evaluated by the integration of the hydrodynamic pressure over the instantaneous wetted body surface. The problem is solved for a uniform circular cylinder by means of the Green’s theorem and semi-analytical solutions are presented. The far field conditions for each order of potentials are proposed to ensure the existence of a unique solution. The restriction on the validation of the solutions is discussed.