Calculation of transverse hydrodynamic coefficients using computational fluid dynamic approach

Computational Fluid Dynamic (CFD) based on Reynolds Averaged Navier–Stokes equation is used for determining the transverse hydrodynamic damping force and moment coefficients that are needed in the maneuverability study of marine vehicles. Computations are performed for two geometrical shapes representing typical AUVs presently in use. Results are compared with available data on similar geometries and from some of the available semi-empirical relations. It is found that the CFD predictions compares reasonable well with these results. In particular, the CFD predictions of forces and moments are found to be nonlinear with respect to the transverse velocity, and therefore both linear and nonlinear coefficients can be derived. A discussion on the sources of the component forces reveal that the total force and moment variations should in fact be nonlinear.     

Wave interaction with a submarine pipeline in clayey soil due to random waves

The wave pressure and uplift force due to random waves on a submarine pipeline (resting on bed, partially buried and fully buried) in clayey soil are measured. The influence of various parameters viz., wave period, wave height, water depth, burial depth and consistency index of the soil on wave pressures around and uplift force on the submarine pipeline was investigated. The wave pressures were measured at three locations around the submarine pipeline (each at 120° to the adjacent one). It is found that the wave pressure and uplift force spectrum at high consistency index of the soil is smaller compared to that of low consistency index. Just burying the pipeline (e/D=1.0) in clayey soil reduces the uplift force to less than 60% of the force experienced by a pipeline resting on the seabed (e/D=0.0) for I_c=0.33.     

On the radiation and diffraction of linear water waves by an infinitely long rectangular structure submerged in oblique seas

The radiation and diffraction of linear water waves by an infinitely long rectangular structure submerged in oblique seas of finite depth is investigated. The analytical expressions for the radiated and diffracted potentials are derived as infinite series by use of the method of separation of variables. The unknown coefficients in the series are determined by the eigenfunction expansion matching method. The expressions for wave forces, hydrodynamic coefficients and reflection and transmission coefficients are given and verified by the boundary element method. Using the present analytical solution, the hydrodynamic influences of the angle of incidence, the submergence, the width and the thickness of the structure on the wave forces, hydrodynamic coefficients, and reflection and transmission coefficients are discussed in detail.     

Wave interaction with a perforated wall breakwater with a submerged horizontal porous plate

This study examines the hydrodynamic performance of a new perforated-wall breakwater. The breakwater consists of a perforated front wall, a solid back wall and a submerged horizontal porous plate installed between them. The horizontal porous plate enhances the stability and wave-absorbing capacity of the structure. An analytical solution based on linear potential theory is developed for the interaction of water waves with the new proposed breakwater. According to the division of the structure, the whole fluid domain is divided into three sub-domains, and the velocity potential in each domain is obtained using the matched eigenfunction method. Then the reflection coefficient and the wave forces and moments on the perforated front wall and the submerged horizontal porous plate are calculated. The numerical results obtained for limiting cases are exactly the same as previous predictions for a perforated-wall breakwater with a submerged horizontal solid plate [Yip, T.L., Chwang, A.T., 2000. Perforated wall breakwater with internal horiontal plate. Journal of Engineering Mechanics ASCE 126 (5), 533–538] and a vertical wall with a submerged horizontal porous plate [Wu, J.H., Wan, Z.P., Fang, Y., 1998. Wave reflection by a vertical wall with a horizontal submerged porous plate. Ocean Engineering 25 (9), 767–779]. Numerical results show that with suitable geometric porosity of the front wall and horizontal plate, the reflection coefficient will be always rather small if the relative wave absorbing chamber width (distance between the front and back walls versus incident wavelength) exceeds a certain small value. In addition, the wave force and moment on the horizontal plate decrease significantly with the increase of the plate porosity.     

Evaluation of bending moments and shear forces at unit connections of very large floating structures using hydroelastic and rigid body analyses

This paper investigates the characteristics of bending moments, shear forces and stresses at unit connections of very large floating structures (VLFS) under wave loads. The responses of VLFS are calculated by solving multi-body motion equation considering hydroelasticity and connection stiffness. Hydroelastic responses are calculated by the direct method. Higher-order boundary element method (HOBEM) is used for fluid analysis and finite element method (FEM) is introduced for structural analysis. The equation of motion is modified to describe the unit connections by employing spring elements. Bending moments and shear forces at the connections are obtained from the dynamic equilibrium condition for pressures and inertia forces. Two types of VLFS units such as tandem arranged units and side-by-side arranged units are considered in the numerical examples. The influences of connection stiffness, wave frequency and heading angle on responses of VLFS are investigated through the numerical examples. Rigid body analysis along with hydroelastic analysis is also carried out in the numerical analysis and comparison of those two approaches is discussed.     

In-line response of a cylinder in oscillatory flow

The most widely used mathematical model to represent flow-induced in-line forces on structures is based on the Morison¹ equation. The present paper investigates the validity of using an extension of Morison's equation for non-stationary structures, by comparing predictions with results from a simple laboratory experiment. An elastically-mounted circular cylinder is placed in the sinusoidal flow of a U-tube, and responds in-line with the flow. Cylinder forces and responses are recorded over a range of Keulegan Carpenter numbers up to 35. An equation of motion is solved simply by using relative coordinates and by employing equivalent linearisation. The linear results are compared over a wide variation of parameters with solutions using the full nonlinear equation. Thereafter experimental results are compared with linear predictions.     

Statistics of wave forces on large horizontal cylinders

To the first order in a Stokes expansion, the pressure force exerted by a sea state on a large horizontal cylinder represents a stationary random Gaussian process. A relationship is obtained between the spectrum of this process and the wave spectrum. As a consequence, the basic statistical properties of the height and period of the individual waves of the force-process are also obtained. It is proven that these statistical properties agree very well with the data from a small scale field experiment.     

Experimental studies on the slowly varying drift motion of a berthed container ship model

The effects of free-surface waves on the floating structures are of great importance in the offshore industry. Among the six degrees of motions of a surface ship the absence of restoring forces in surge, sway and yaw led to critical situations for moored ships in the recent times. The order of forces in horizontal plane and their exciting frequencies are matters of interest. The resonance with the presence of moored chains led to many accidents in the recent past. The lines in dry conditions may not give good damping and in wet condition they may trigger the system to chaotic motions and jumps. Two different loading conditions of a container ship model are tested with waves in laboratory conditions in two different drafts. The mooring lines are chosen as per scale law and the energy under the response spectrum is determined from the plots. The results give new insights into the movement of a berthed ships subjected to waves. Response of the moored ship to different loading conditions in different water depths are discussed in this paper. The paper gives the order of energy due to first-order and slowly varying movement of a berthed container model in a towing tank.     

Drag force on a circular cylinder in unseparated laminar high Reynolds number nonlinear random oscillatory flow

The stochastic properties of the drag force maxima on a circular cylinder subjected to nonlinear random waves are investigated. Unseparated laminar high Reynolds number flow is considered. A simplified approach based on second order Stokes waves is presented, including the sum-frequency effect only. It is demonstrated how a drag force formula valid for regular linear waves can be used to find the cumulative distribution function of individual drag force maxima for nonlinear irregular waves. Here the [Wang, 1968] drag force coefficient is used.