Hull component interaction and scaling for TLP hydrodynamic coefficients

The purpose of this paper is to validate a new method that can be used by offshore platform designers to estimate the added mass and hydrodynamic damping coefficients of potential Tension Leg Platform hull configurations. These coefficients are critical to the determination of the platform response particularly to high frequency motions in heave caused by sum-frequency wave forcing i.e. “springing”. Previous research has developed the means by which offshore platform designers can extrapolate anticipated full-scale hydrodynamic coefficients based on the response of individual model scale component shapes. The work presented here further evaluates the component scaling laws for a single vertical cylinder and quantifies the effects due to hydrodynamic interaction. Hydrodynamic interaction effects are established through a direct comparison between the superposition of individual hull component coefficients and those evaluated directly from complete hull configuration models. The basis of this comparison is established by the experimental evaluation of the hydrodynamic coefficients for individual hull components as well as partial and complete platform models. The results indicate that hydrodynamic interaction effects between components are small in heave, and validate component scaling and superposition as an effective means for added mass and damping coefficient estimation of prototype platforms. It is found that the dependency of damping ratio with KC for a TLP is almost identical to that of a single column, thus offering a scaling methodology for prototype damping ratio values.     

Linear analysis of air cushion vehicle seakeeping response

A linearized analysis of the response of an air cushion vehicle running in waves is described. The analysis uses the linear systems approach where the vehicle is considered to be a “black box”, i.e. the response characteristics are determined experimentally from input-output relationships. The wave forces and moments are expressed in a form that produces the proper limiting behavior for infinite wavelength. Predicted motion response is shown to compare well with experimental data.     

Evaluation of the physical process controlling beach changes adjacent to nearshore dredge pits

Numerical modeling of a beach nourishment project is conducted to enable a detailed evaluation of the processes associated with the effects of nearshore dredge pits on nourishment evolution and formation of erosion hot spots. A process-based numerical model, Delft3D, is used for this purpose. The analysis is based on the modification of existing bathymetry to simulate “what if” scenarios with/without the bathymetric features of interest. Borrow pits dredged about 30 years ago to provide sand for the nourishment project have a significant influence on project performance and formation of erosional hot spots. It was found that the main processes controlling beach response to these offshore bathymetric features were feedbacks between wave forces (roller force or alongshore component of the radiation stress), pressure gradients due to differentials in wave set-up/set-down and bed shear stress. Modeling results also indicated that backfilling of selected borrow sites showed a net positive effect within the beach fill limits and caused a reduction in the magnitude of hot spot erosion.     

The discrete methods for free vibration analyses of an immersed beam carrying an eccentric tip mass with rotary inertia

In this paper, a beam without contact with water is called the “dry” beam and the one in contact with water is called the “wet” beam. For a partially (or completely) immersed uniform beam carrying an eccentric tip mass possessing rotary inertia, the conventional analytical (closed-form) solution is achieved by considering the inertial forces and moments of the tip mass and rotary inertia as the boundary conditions at the tip end of the beam. However, it has been found that the approximate solution for the last problem may be achieved by two techniques: Method 1 and Method 2. In Method 1, the basic concept is the same as the conventional analytical method; but in Method 2, the tip end of the beam is considered as a free end, while the inertial forces and moments induced by the tip mass and rotary inertia are considered as the external loads applied at the tip end of the beam. The main differences between the formulation of Method 1 and that of Method 2 are: In Method 1, the “normal” shapes of the “dry” beam are functions of the frequency-dependent boundary conditions but the external loads at the tip end are equal to zero; On the contrary, in Method 2, the “normal” mode shapes of the “dry” beam are determined based on the zero boundary conditions at the tip end of the beam but the external loads at the tip end due to the inertial effects of the tip mass and rotary inertia must be taken into consideration for the free vibration analysis of the “wet” beam. Numerical results reveal that the approximate solution obtained from Method 2 are very close to that from Method 1 if the tip mass moment of inertia is negligible. Besides, the two approximate solutions are also very close to the associated analytical (closed-form) solution or the finite element solution. In general, it is hoped that there exist several methods for tackling the same problem so that one may have more choices to incorporate with the specified cases. It is believed that the two approximate methods presented in this paper will be significant from this point of view.     

On the nonlinear hydrodynamic forces for a ship advancing in waves

In this paper, using a second-order steady-state approach and a three-dimensional (3D) pulsating source distribution method derives the nonlinear hydrodynamic forces on a ship advancing in waves. The nonlinear hydrodynamic forces considered here consist of the mean lateral drifting force and the added resistance, which can be expressed as products of the ship-motion responses, the radiation potential, diffraction potential and the incident-wave potential. All related velocity potentials applied in the calculations are in 3D form. The Series 60 and Marine ship hulls are used for numerical calculations and the results are compared with existing experimental data and two-dimensional (2D) solutions. The comparisons show that the results obtained in the paper generally agree with experimental data well. It is also found that the nonlinear hydrodynamic forces obtained based on the present 3D source distribution methods are indeed improved in some calculations compared with the 2D method, especially for the mean lateral drifting force.     

Sensitivity of AUV response to variations in hydrodynamic parameters

The sensitivity of the response of a typical AUV to changes in hydrodynamic parameters is examined. The analysis is primarily performed using a computer model of an axi-symmetric vehicle typical of many AUVs in service today. The vehicle used is the Canadian Self-Contained Off-the-shelf Underwater Testbed (C-SCOUT), designed and built by graduate and work term students. The fully nonlinear computer model is based on Newton–Euler equations of motion, and uses the component build-up method to describe the excitation forces. The hydrodynamic parameters are varied in a series of simulations with the computer model; the response being analyzed for specific performance indicators.     

Hydrodynamic interactions and relative motions of two floating platforms with mooring lines in side-by-side offloading operation

The hydrodynamic interaction and mechanical coupling effects of two floating platforms connected by elastic lines are investigated by using a time-domain multi-hull/mooring/riser coupled dynamics analysis program. Particular attention is paid to the contribution of off-diagonal hydrodynamic interaction terms on the relative motions during side-by-side offloading operation. In this regard, the exact method (CMM: combined matrix method) including all the vessel and line dynamics, and the 12×12 hydrodynamic coefficients in a combined matrix is developed. The performance of two typical approximation methods (NHI/No Hydrodynamic Interaction: iteration method between two vessels without considering hydrodynamic interaction effects; SMM/Separated Matrix Method: iteration method between two vessels with partially considering hydrodynamic interaction effects, i.e. ignoring off-diagonal cross-coupling terms in the 12×12 hydrodynamic coefficient matrix) is also tested for the same side-by-side offloading operation in two different environmental conditions. The numerical examples show that there exists significant discrepancy at sway and roll modes between the exact and the approximation methods, which means that the cross-coupling (off-diagonal block) terms of the full hydrodynamic coefficient matrix play an important role in the case of side-by-side offloading operation. Therefore, such approximation methods should be used with care. The fender reaction forces, which exhibit large force with contact but no force without contact, are also numerically modeled in the present time-domain simulation study.     

Hydrodynamic Coefficients and Wave Excitation Forces for A Ship near A Quay

In this paper,the effects of a quay or a solid jetty on hydrodynamic coefficients and vertical wave excitation forces on a ship woth or without forward speed are discussed.A modified simple Green function technique is used to calculate the 2D coefficients while the strip theory is used to calculate the 3D coefficients. Wave excitation forces are also calculated with the strip theory. Numerical results are provided for hydrodynamic coefficients and vertical wave excitation forces on a 200000 DWT tanker ship. It is found that the quay has a considerable effect on the hydrodynamic coefficients and wave excitation forces for a ship.     

An effective wave-trapping system

This is a theoretical study of a breakwater-seawall wave-trapping system. The breakwater, being flexible, porous and thin beam-like, is held fixed in the sea bed and idealized as one-dimensional beam of uniform flexural rigidity and uniform mass per unit length. The seawall, being vertical, rigid and impermeable, is located behind the breakwater by a distance of L. The velocity potentials of the wave motion are coupled with the equation of motion of the breakwater. Analytical solutions in closed forms are obtained for the reflected and transmitted velocity potentials together with the displacement of the breakwater. The free-surface elevation, hydrodynamic forces acting on both the breakwater and the seawall are determined. It is found that the values of L, at which the minimum reflected-wave amplitudes reach, are in the range of λ to λ for breakwaters with different rigidity and permeability. It is shown that, when the spacing L maintains values in the range of λ to λ, the resultant amplitudes in both regions can be reduced to a favorable amount for any wave and structural parameters. It is also shown that the hydrodynamic forces on the breakwater decrease as the structural flexibility and porosity increase. However, with increases of the structural porosity and flexibility, the seawall experiences an increase of the hydrodynamic forces. Various results are presented in this paper to illustrate the effects of the structural and perous parameters together with the spacing on the response and efficiency of the breakwater-seawall wave-trapping system.     

Tracking the last sea-level cycle: seafloor morphology and shallow stratigraphy of the latest Quaternary New Jersey middle continental shelf

Seafloor geomorphology and surficial stratigraphy of the New Jersey middle continental shelf provide a detailed record of sea-level change during the last advance and retreat of the Laurentide ice sheet (120 kyr B.P. to Present). A NW–SE-oriented corridor on the middle shelf between water depths of 40 m (the mid-shelf “paleo-shore”) and 100 m (the Franklin “paleo-shore”) encompasses 500 line-km of 2D Huntec boomer profiles (500–3500 Hz), an embedded 4.6 km² 3D volume, and a 490 km² swath bathymetry map. We use these data to develop a relative stratigraphy. Core samples from published studies also provide some chronological and sedimentological constraints on the upper <5 m of the stratigraphic succession.The following stratigraphic units and surfaces occur (from bottom to top): (1) “R”, a high-amplitude reflection that separates sediment >46.5 kyr old (by AMS ¹⁴C dating) from overlying sediment wedges; (2) the outer shelf wedge, a marine unit up to 50 m thick that onlaps “R”; (3) “Channels”, a reflection sub-parallel to the seafloor that incises “R”, and appears as a dendritic system of channels in map view; (4) “Channels” fill, the upper portion of which is sampled and known to represent deepening-upward marine sediments 12.3 kyr in age; (5) the “T” horizon, a seismically discontinuous surface that caps “Channels” fill; (6) oblique ridge deposits, coarse-grained shelly units comprised of km-scale, shallow shelf bedforms; and (7) ribbon-floored swales, bathymetric depressions parallel to modern shelf currents that truncate the oblique ridges and cut into surficial deposits.We interpret this succession of features in light of a global eustatic sea-level curve and the consequent migration of the coastline across the middle shelf during the last 120 kyr. The morphology of the New Jersey middle shelf shows a discrete sequence of stratigraphic elements, and reflects the pulsed episodicity of the last sea-level cycle. “R” is a complicated marine/non-marine erosional surface formed during the last regression, while the outer shelf wedge represents a shelf wedge emplaced during a minor glacial retreat before maximum Wisconsin lowstand (i.e., marine oxygen isotope stage 3.1). “Channels” is a widespread fluvial subarial erosion surface formed at the late Wisconsin glacial maximum 22 kyr B.P. The shoreline migrated back across the mid-shelf corridor non-uniformly during the period represented by “Channels” fill. Oblique ridges are relict features on the New Jersey middle shelf, while the ribbon-floored swales represent modern shelf erosion. There is no systematic relationship between modern seafloor morphology and the very shallowly buried stratigraphic succession.     

Hydrodynamic forces on a partially submerged cylinder at high Reynolds number in a steady flow

The hydrodynamic forces on the stationary partially submerged cylinder are investigated through towing test with Reynolds number ranging from 5 × 10⁴ to 9 × 10⁵. Three test groups of partially submerged cylinders with submerged depths of 0.25 D, 0.50 D, and 0.75 D and one validation group of fully submerged cylinders are conducted. During the experiments, the hydrodynamic forces on the cylinders are measured using force sensors. The test results show a considerable difference in the hydrodynamic coefficients for the partially submerged cylinders versus the fully submerged cylinders. A significant mean downward lift force is first observed for the partially submerged cylinders in a steady flow. The maximum of the mean lift coefficients can reach 1.5. Two distinct features are observed due to the effects of overtopping: random distributions in the mean drag coefficients and a clear quadratic relationship between the mean lift coefficients and the Froude number appear in the non-overtopping region. However, the novel phenomenon of a good linear relationship with the Froude number for the mean hydrodynamic coefficients is clearly shown in the overtopping region. In addition, fluctuating hydrodynamic coefficients are further proposed and investigated. These results are helpful to have a better understanding of the problem and to improve related structural designs.     

The calculation of zig-zag maneuver in regular waves with use of the impulse response functions

The traditional governing equations for sway–yaw maneuvering motion are a set of ordinary differential equations with constant coefficients. But, as is well known, integro–differential equations with impulse response functions are more strict governing equations that can handle the frequency dependence of hydrodynamic forces.In this paper, the two types of equation are compared and used to calculate the 10°–10° zig-zag maneuver in waves. Differences between the solutions are discussed.     

Interactions between fully nonlinear water waves and cylinder arrays in a wave tank

Fully nonlinear interactions between water waves and vertical cylinder arrays in a numerical tank are studied based on a finite element method (FEM). The three-dimensional (3D) mesh is constructed through an extension of a 2D Delaunay surface grid along the vertical line. The velocity potential is obtained by solving a linear matrix system of FEM, and a difference scheme is then used to calculate the velocity on the free surface to track its movement. Waves and hydrodynamic forces are obtained for both bottom mounted and truncated cylinders. The simulations have provided many results to show the nature of mutual interference between cylinders in arrays and its effects on waves and forces at the nearly trapped mode frequency. The effect of the tank wall on waves and forces has been investigated, and the nonlinear features of waves and forces have also been discussed.     

Hydrodynamic behavior of a straight floating pipe under wave conditions

This paper examines the hydrodynamic behavior of a floating straight pipe under wave conditions. The main problem in calculating the forces acting on a small-sized floating structure is obtaining the correct force coefficients C_n and C_t, which differ from a submerged structure. For a floating straight pipe of small size, we simplify it into a 2D problem, where the pipe is set symmetrically under wave conditions. The force equations were deduced under wave conditions and a specific method proposed to resolve the wave forces acting on a straight floating pipe. Results of the numerical method were compared to those from model tests and the effects of C_n and C_t on numerical results studied. Suggestions for the selection of correct C_n and C_t values in calculating wave forces on a straight floating pipe are given. The results are valuable for research into the hydrodynamic behavior of the gravity cage system.     

Interaction between water flow and oxygen deficiency on growth in the infaunal brittle star Amphiura filiformis (Echinodermata: Ophiuroidea)

Interactions between ‘oxygen concentration’ (normoxia: >80% oxygen saturation, and hypoxia: 18% oxygen saturation) and ‘water flow velocity’ (low: 0.1 cm s⁻¹, and moderate: 0.5 cm s⁻¹) were studied on growth rates in the brittle star Amphiura filiformis in a flow-through aquaria system. Effects of ‘sublethal predation’ on growth rates were investigated as ‘number of amputated arms’ (1 and 3 arms) and ‘amputation of the disk’. A significant interaction between oxygen concentration and water flow velocity was observed in mean arm regeneration rate, but in both flow velocities higher mean arm regeneration rates were observed in normoxia compared to hypoxia. In hypoxia a positive response in arm regeneration rate was observed in moderate flow compared to low flow velocity. In normoxia, however, no response to flow velocity was observed. The latter observation indicates that Amphiura filiformis is able to maintain the ventilation of the burrow at low flow velocities, but in low oxygen concentrations hydrodynamic forces seem to affect growth. A significant interaction between oxygen concentration and disk amputation was observed in both arm and disk regeneration rates, indicating that the disk is the major organ for gas exchange in this species. The number of arms amputated, however, did not affect mean arm regeneration rate. The results obtained in this study suggest that the secondary production in subtidal infaunal populations could be negatively affected by low oxygen concentrations and that this response is even more negative in combination with low flow velocities in the near-bottom water.     

Coupled dynamics of tethered buoy systems

The three-dimensional coupled behavior during the interaction of buoys with their mooring systems is numerically analyzed. A time-domain model was developed to predict the response of a tethered buoy subject to hydrodynamic loadings. External loadings include hydrodynamic forces, tethers tensions, wind loadings and weight. System nonlinearities include large rotational and translational motions, and non-conservative fluid loadings. The mooring problem is formulated as a combined nonlinear initial-value and two-point-boundary-value problem which is directly integrated both in time and space. Buoy equations of motion are derived using small Eulerian angles. Coupling between rotational and translational degrees of freedom is included and coupling between the buoy and cable is effected by adopting the buoy equations of motion as boundary conditions at one end for the mooring problem. Numerical examples are provided to validate the formulation and solution technique; predicted responses of three types of buoy (sphere, spar, and disc) are compared with experimental results.     

An experimental investigation of hydrodynamic coefficients for a vertical truncated rectangular cylinder due to regular and random waves

The research into hydrodynamic loading on ocean structures has concentrated mostly on circular cross-section members and relatively limited work has been carried out on wave loading on other cross-sections such as rectangular sections. These find applications in many offshore structures as columns and pontoons in semi-submersibles and tension-leg platforms. The present investigation demonstrates the behaviour of rectangular cylinders subject to wave loading and also supplies the hydrodynamic coefficients for the design of these sections.This paper presents the results of wave forces acting on a surface piercing truncated rectangular cylinder set vertically in a towing tank. The experiments are carried out in a water depth of 2.2 m with regular and random waves for low Keulegan–Carpenter number up to 6. The rectangular cylinder is of 2 m length, 0.2 m breadth and 0.4 m width with a submergence depth of 1.45 m from still water level. Based on Morison equation, the relationship between inertia and drag coefficients are evaluated and are presented as a function of KC number for various values of frequency parameter β, for two aspect ratios of cylinders, equals to 1/2 and 2/1. Drag and inertia coefficients obtained through regular wave tests are used for the random wave analysis to compute the in-line force spectrum.The results of the experiments show the drag and inertia coefficients are strongly affected by the variation in the aspect ratios of the cylinder. The drag coefficients decreases and inertia coefficients increases with increase in Keulegan–Carpenter number up to the range of KC number tested. The random wave results show a good correlation between measured and computed force spectrums. The transverse forces in both regular and random waves are found to be small compared to in-line forces.     

The effects of LNG-tank sloshing on the global motions of LNG carriers

The coupling and interactions between ship motion and inner-tank sloshing are investigated by a time-domain simulation scheme. For the time-domain simulation, the hydrodynamic coefficients and wave forces are obtained by a potential-thoery-based three-dimensional (3D) diffraction/radiation panel program in frequency domain. Then, the corresponding simulations of motions in time domain are carried out using convolution integral. The liquid sloshing in a tank is simulated in time domain by a Navier–Stokes solver. A finite difference method with SURF scheme is applied for the direct simulation of liquid sloshing. The computed sloshing force and moment are then applied as external excitations to the ship motion. The calculated ship motion is in turn inputted as the excitation for liquid sloshing, which is repeated for the ensuing time steps. For comparison, we independently developed a coupling scheme in the frequency domain using a sloshing code based on the linear potential theory. The hydrodynamic coefficients of the inner tanks are also obtained by a 3D panel program. The developed schemes are applied to a barge-type FPSO hull equipped with two partially filled tanks. The time-domain simulation results show similar trend when compared with MARIN's experimental results. The most pronounced coupling effects are the shift or split of peak-motion frequencies. It is also found that the pattern of coupling effects between vessel motion and liquid sloshing appreciably changes with filling level. The independent frequency-domain coupled analysis also shows the observed phenomena.     

A metamodel-based towed system simulation

The objective of this exercise was the development of a computer simulation of a US Navy towed system (towed body and line array) capable of near real-time predictive capabilities. The purpose of the computer simulation was to be able to determine the lateral motion of the towed body in response to ship maneuvers. The theoretical approach was to develop a spatial-domain computer simulation of each of the towed system components treated as a system, and then develop a “metamodel” of the response by using simple algebraic expressions. At-sea trials were conducted aboard US Navy vessels to verify the simulation and fine-tune its performance.