Prediction of hydrodynamic loading on a mini TLP with free surface effects

This paper describes the extension of a fluid-flow simulations method to capture the free surface evolution around a full-scale Tension Leg Platform (TLP). The focus is on the prediction of the resulting hydrodynamic loading on the various elements of the TLP in turbulent flow conditions and, in particular, on quantifying the effects of the free surface distortion on this loading. The basic method uses finite-volume techniques to discretize the differential equations governing conservation of mass and momentum in three dimensions. The time-averaged forms of the equations are used, and the effects of turbulence are accounted for by using a two-equation, eddy-viscosity closure. The method is extended here via the incorporation of surface-tracking algorithm on a moving grid to predict the free-surface shape. The algorithm was checked against experimental measurements from two benchmark flows: the flow over a submerged semi-circular cylinder and the flow around a floating parabolic hull. Predictions of forces on a model TLP were then obtained both with and without allowing for the deformation of the free surface. The results suggest that the free surface effects on the hydrodynamic loads are small for the values of Froude number typically encountered in offshore engineering practice.     

Numerical wave tank computations of nonlinear motions of two-dimensional arbitrarily shaped free floating bodies

Time domain simulations of nonlinear motions of two-dimensional floating bodies in waves are presented. The so called `body exact' approach is adopted in a numerical wave tank. A new scheme for pressure evaluation on the wetted hull is developed and systematically used with good results in terms of accuracy and stability. Strongly flared geometries are successfully handled even at very large amplitude motions. The validation of the code is carried out according to the 20th ITTC Seakeeping Committee recommendations through internal checks of consistency and through comparisons with available experimental data.     

Performance analysis of 3D hydrofoil under free surface

The purpose of the present paper is to develop a potential-based panel method for determining the steady potential flow about three-dimensional hydrofoil under free surface. The method uses constant-strength doublets and source density distribution over the foil body surface and thereby Dirichlet-type boundary condition is used instead of Neumann-type condition. On the undisturbed free surface source density is used to meet the free surface condition that is linearised in terms of double-body model approach and is discretised by a one-side, upstream, four-point finite difference operator. After solving the doublets on the foil and sources on the free surface, the numerical results of pressure, lift and resistance coefficients and also wave profiles can then be calculated for different Froude number and depth of submergence to demonstrate the influence of free surface and aspect ratio effects on performance of the hydrofoil.     

Adaptive depth controller design for a submerged body moving near free surface

A submerged body that moves near a free surface needs to keep its attitude and position to accomplish its missions, which are required to validate the performance of a designed controller before sea trial. Hydrodynamic maneuvering coefficients are generally obtained by experiments or computational fluid dynamics, but these coefficients suffer from uncertainty. Environmental loads such as wave excitation, current, and suction forces act on the submerged body when it moves near the free surface. Therefore, a controller for the submerged body should be robust to parameter uncertainty and environmental loads. In this paper, six-degree-of-freedom equations of motion for the submerged body are constructed. An adaptive control method based on the neural network and proportional–integral–derivative controller is used for the depth controller. Simulations are performed under various depth and environmental conditions, and the results show the effectiveness of the designed controller.     

The effect of appendages on the hydrodynamic characteristics of an underwater vehicle near the free surface

An underwater vehicle typically has various appendages such as sail, rudders and hydroplanes. These appendages affect the hull hydrodynamic characteristics, including the resistance components and the form of the generated wave due to the motion of the vehicle near the free surface. The effect of the appendages on the hydrodynamic characteristics of an underwater vehicle near the free surface is studied. Initially the DARPPA SUBOFF submarine without the appendages is selected and hydrodynamic characteristics, including the friction resistance, viscous pressure resistance, wave resistance and shape of the created wave on the free surface are calculated for Froude numbers in the range of 0.128–0.84 and non-dimensional submergence depths 1.3, 2.2, 3.3 & 4.4. Then, by adding the appendages and comparing these two conditions, the effect of appendages is obtained. The results of computations indicate that the appendages cause a mean increase of about 16% in the total resistance. This increment is due to viscosity of fluid and also the interaction of the main hull with the appendages. There are no significant changes in the wave pattern and wave making resistance due to the presence of appendages.     

Experimental and numerical investigation of sloshing using different free surface capturing methods

We investigated the use of numerical methods to predict liquid sloshing phenomena in a moving tank and compared our results to model test measurements. The numerical techniques for the free surface, based on the so-called finite Volume-of-Fluid (VoF) approach, comprised an incompressible VoF method, an incompressible coupled Level-Set and Volume-of-Fluid (clsVoF) method, and a compressible VoF method. We assessed the capability of these three numerical methods to achieve suitable numerical predictions of sloshing phenomena, specifically, air pockets and bubbles on the free surface inside a test tank. To observe the described sloshing phenomena, we simulated tank motions leading to well defined single impact wave motions. We performed repeated physical tests for validation purposes. Computed velocity and pressure time histories were compared to experimental data we obtained from Particle Image Velocimetry (PIV) and pressure sensor measurement. Grid sensitivity and turbulence model studies were performed. We demonstrated that the compressible VoF method was the most suitable method to obtain accurate predictions of sloshing phenomena.     

Studies on an algorithm to control the roll motion using active fins

The very purpose of attaching fins to the hull is to reduce the roll motions of a ship. Roll minimization is a requisite for various operations in the seas. The presence of fin system provides enhanced state of stabilization especially when the vessel is performing a fast maneuvering amidst rough environmental disturbance. The fins in turn are activated by electro-hydraulic mechanism based on the in-built intelligence as per control theory like proportional–integral–derivative (PID) or fuzzy logic. As per this paper, fin system is activated using PID control algorithm. A frigate-type warship is considered for the demonstration purpose. Nonlinear roll motions are controlled using active fins. Lift characteristics of the fins in hydrodynamic flow were studied using CFD package fluent.Good amount of reduction in roll amplitude is achieved from various simulations in random sea. The approach can be used for any irregular sea conditions.     

A finite element model of interaction between viscous free surface waves and submerged cylinders

This paper describes the simulation of the flow of a viscous incompressible Newtonian liquid with a free surface. The Navier–Stokes equations are formulated using a streamline upwind Petrov–Galerkin scheme, and solved on a Q-tree-based finite element mesh that adapts to the moving free surface of the liquid. Special attention is given to fitting the mesh correctly to the free surface and solid wall boundaries. Fully non-linear free surface boundary conditions are implemented. Test cases include sloshing free surface motions in a rectangular tank and progressive waves over submerged cylinders.     

Simulating nonlinear waves on the free surface in surf zones with two-dimensional sloping beach

Unsteady nonlinear wave motions on the free surface in shallow water and over slopes of various geometries are numerically simulated using a finite difference method in rectangular grid system. Two-dimensional Navier–Stokes equations and the continuity equation are used for the computations. Irregular leg lengths and stars are employed near the boundaries of body and free surface to satisfy the boundary conditions. Also, the free surface which consists of markers or segments is determined every time step with the satisfaction of kinematic and dynamic free surface conditions. Moreover, marker-density method is also adopted to allow plunging jets impinging on the free surface. Either linear or Stokes wave theory is employed for the generation of waves on the inflow boundary. For the simulation of wave breaking phenomena, the computations are carried out with various wave periods and sea bottom slopes in surf zone. The results are compared with other existing computational and experimental results. Agreement between the experimental data and the computation results is good.     

URANS investigation of the interaction between the free surface and a shallowly submerged underwater vehicle at steady drift

An axisymmetric underwater vehicle (UV) at a steady drift angle experiences the complex three-dimensional crossflow separation. This separation arises from the unfavorable circumferential pressure gradient developed from the windward side toward the leeward side. As is well known, the separated flow in the leeward side gives rise to the formation of a pair of vortices, which affects considerably the forces and moments acting on the UV. In this regard, the main purpose of the present study is to evaluate the role of the leeward vortical flow structure in the hydrodynamic behavior of a shallowly submerged UV at a moderate drift angle traveling beneath the free surface. Accordingly, the static drift tests are performed on the SUBOFF UV model using URANS equations coupled with a Reynolds stress turbulence model. The simulations are carried out in the commercial code STARCCM+ at a constant advance velocity based on Froude number equal to F_n = 0.512 over submergence depths and drift angles ranging from h = 1.1D to h = ∞ and from β = 0 to β = 18.11°, respectively. The validation of the numerical model is partially conducted by using the existing experimental data of the forces and moment acting on the totally submerged bare hull model. Significant interaction between the low-pressure region created by the leeward vortical flow structure and the free surface is observed. As a result of this interaction, the leeward vortical flow structure appears to be largely responsible for the behavior of the forces and moments exerted on a shallowly submerged UV at steady drift.     

波面位移非线性特征数值研究

基于Longuest-Higgins(1963)非线性海浪模型,在有限水深且存在均匀背景流的条件下,根据Song(2006)给出的波面位移二阶表达式,采用Combi海浪频谱计算了海表面定点波面位移时间序列和波面位移概率统计分布。分析了波面位移统计分布随风速、水深、反波龄和均匀背景流的变化特征和规律以及不同海况条件下二阶非线性项对波面位移统计分布的影响。结果表明:二阶非线性项使波面位移分布偏离正态分布,二阶非线性作用受风速、水深、反波龄和均匀背景流的影响。风速增大、水深降低、反波龄减小或者均匀背景流和风速传播方向相反均使波面位移二阶非线性项的作用加强,无因次波面位移概率密度分布的偏度和峰度随之增大,反之则二阶非线性项作用减弱。当均匀背景流和风速相同时,虽然使非线性项的作用减弱,但平均波面位移反而比静止水平面降低。当均匀背景流和风速相反时,虽然使非线性作用增强,但平均波面位移反而趋于静止水平面。得到如下结论:二阶非线性项对于波面位移有显著影响,数值模拟波面位移需要增加二阶非线性项。通过以上研究,提高了数值模拟波面位移的准确性,而波面位移是海浪最基本的特征量,从而增强了海浪模拟和预报的准确性,对海洋工程、海–气相互作用、上层海洋动力学等具有重要意义。     

Improved assessments of wave-induced fatigue for free spanning pipelines

For subsea pipeline projects, the costs related to seabed correction and free span intervention are often considerable. Development of reliable methods for fatigue analyses of pipelines in free spans contributes to minimize costs without compromising pipeline integrity. Assessment of wave-induced fatigue damage on multi-span pipelines is investigated, and improved analysis methods are suggested in this paper. A time-domain (TD) algorithm is developed, which accounts for non-linear hydrodynamic loading and dynamic interaction between adjacent spans. The proposed TD approach is employed to evaluate linearized frequency-domain (FD) solutions from recognized design standards and to study the dynamic response of multi-span pipelines to direct wave loading. Differences between multi- and single-span analyses are described for the first time, and the common assumption that the main fatigue damage contribution comes from the fundamental mode is demonstrated not to hold for multi-spans. An improved FD solution capable of predicting multi-mode response is derived and demonstrated to give accurate fatigue life estimates for multi-span pipelines.     

Computation of solitary waves during propagation and runup on a slope

A numerical time-simulation algorithm for analysing highly nonlinear solitary waves interacting with plane gentle and steep slopes is described by employing a mixed Eulerian–Lagrangian method. The full nonlinear free surface conditions are considered here in a Lagrangian frame of reference without any analytical approximations, and thus the method is valid for very steep waves including overturning. It is found that the runup height is crucially dependent on the wave steepness and the slope of the plane. Pressures and forces exerted on impermeable walls of different inclinations (slopes) by progressive shallow water solitary waves are studied. Strong nonlinear features in the form of pronounced double peaks are visible in the time history of pressure and force signals with increasing heights of the oncoming solitary waves. The effect of nonlinearity is less pronounced as the inclination of the wall decreases with respect to the bottom surface.     

Viscous free surface effect on coastal embankment hydrodynamics

A finite-differnece method was used to calculate the nonlinear hydrodynamic pressures acting on the coastal embankment faces by seismic-wave actions. The nonlinearity of free surface flow, convective acceleration, viscosity and surface tension of fluid are included in the analysis. The kinematic and dynamic free surface boundary conditions are employed for calculating the horizontal fluid velocity, pressure at the free surface and the surface profile of the fluid. The time-dependent water surface is transformed to the horizontal plane, and the flow field is mapped onto a rectangular, making it convenient to model the complex sea bottom geometry and the wavy water surface by the finite-difference method. Fully nonlinear and weakly nonlinear dynamic free surface conditions are used and compared. The effects of surface tension of fluid are also discussed. The nonslip boundary condition is applied on the most part of the interface between fluid and solid face, except the region near the intersection between free surface and wall face. The numerical results are presented for various water depths and ground motion intensities, and their associate viscous effects on coastal embankment hydrodynamics are discussed.     

On a near-optimal control approach for a wave energy converter in irregular waves

Real-time smooth reactive control and optimal damping of wave energy converters in irregular waves is difficult in part because the radiation impulse response function is real and causal, which constrains the frequency-dependent added mass and radiation damping according to the Kramers–Kronig relations. Optimal control for maximum energy conversion requires independent synthesis of the impulse response functions corresponding to these two quantities. Since both are non-causal (one being odd and other even), full cancellation of reactive forces and matching of radiation damping requires knowledge or estimation of device velocity into the future. To address this difficulty and the non-causality of the exciting force impulse response function, this paper investigates the use of propagating-wave surface elevation up-wave of the device to synthesize the necessary forces. Long-crested waves are assumed, and the approach is based on the formulations of Naito and Nakamura [2] and Falnes [22]. A predominantly heaving submerged device comprised of three vertically stacked discs driving a linear power take-off is studied. The overall formulation leads to smooth control that is near-optimal, given the approximations involved in the time-shifting of the non-causal impulse response functions and the consequent up-wave distances at which wave surface elevation is required. Absorbed power performance with the near-optimal approach is compared with two other cases, (i) when single-frequency tuning is used based on non-real time adjustment of the reactive and resistive loads to maximize conversion at the spectral peak frequency, and (ii) when no control is applied with damping set to a constant value. Simulation results for wave spectra over a range of energy periods and significant wave heights are compared for the three situations studied. While practical implementation presents engineering challenges, in terms of time-averaged absorbed power, unconstrained near-optimal control is found to perform significantly better than single-frequency tuning in the spectra with longer energy periods (>10 s for the present device), and somewhat better in the spectra with shorter energy periods (here ≤10 s).     

Experimental and numerical investigation of a freefall wedge vertically entering the water surface

Experiments and numerical methods are developed to investigate the water entry of a freefall wedge with a focus on the evolution of the pressure on the impact sides (the side contacting water) and the top side (the dry side on the top of the wedge), evolution of the global hydrodynamic loads, evolution of the air–water interface, and wedge motion. It is found that a typical water entry of a freefall wedge can be divided into slamming, transition, collapse and post-closure stages. A single-fluid numerical model is presented to simulate the first three stages. The results are compared to experiments and good agreements are obtained. A two-fluid BEM is proposed to investigate the influence of the air flow before the closure of the cavity created on the top of the wedge. It is found that for the closure of the 2D cavity, the air flow starts to play an important role just before closure but due to the short duration, the influence of air flow on the body velocity and configuration of the air–water interface is limited.     

On the response of a free span pipeline subjected to ocean currents

A mechanistic study is performed to examine the coupling between the in-line and the cross-flow motion of a cylindrical structure subjected to current forces. The structure represents a free span pipeline but concerns marine risers as well.A time domain model is formulated in which the in-line and cross-flow deflections are coupled through the axial tension which in turn is computed from the pipeline prolongation at any time. This formulation introduces time dependent tensions and non-linearity into the problem.Preliminary validation of the model simulations vs. physical test data are carried out for one specific case to ensure that the sag and the in-line deflection are correctly resolved by the model. Using this as the initial condition a series of calculations are carried out to examine cross-flow induced deflections induced by an in-line prescribed deflection and vice versa. Finally, an idealistic simulation of flow induced vibration is presented.The model simulations demonstrate that the coupling varies with the mode shape and with which component it is initially introduced into. However, it is evident that the coupling effects may be significant and not negligible.     

Nonlinear heave radiation forces on two-dimensional single and twin hulls

A study of nonlinear heave radiation of two-dimensional single and double hulls has been carried out in the time domain. The problem is analyzed by means of a fully nonlinear mathematical model, referred to as the mixed Eulerian–Lagrangian (MEL) model, which is based on an integral relation formulation coupled with time-integration of the nonlinear free-surface boundary conditions. The integral equation solver is based on a cubic-spline boundary-element scheme in which both potential and velocity continuity conditions can be enforced through the intersection points. The body undergoes periodic forced heave oscillation. By implementing effective wave-absorbing beaches at the two ends of the rectangular numerical tank, long-term steady-state force-histories could be achieved consistently in all computations.Results in terms of radiation forces for rectangular and triangular single- and twin-hull geometries are presented and discussed. Linear hydrodynamic forces in terms of added-mass and damping are validated for the rectangular hull. The Fourier-analyzed results reveal the extent of nonlinear (higher-order) components in the force-signals over different parameters which include the amplitudes of oscillation, hull-spacing for the twin-hulls and water depth.