Wave force coefficients for horizontally submerged rectangular cylinders

The results of wave force measurements carried out on a section of horizontally submerged rectangular cylinders, which are used as pontoons in many offshore structures, are reported in this paper. Two rectangular cylinders with aspect (depth–breadth) ratios equal to $\frac{1}{2}$ and $\frac{3}{4}$ and a square section (aspect ratio=1.0) cylinder are chosen for this study. Experiments are carried out in a wave tank at a water depth of 2.2 m at low Keulegan–Carpenter (KC) numbers to measure the horizontal and vertical wave forces acting on a 100 mm section, located at mid-length of the cylinders. For each cylinder, tests are carried out for two relative depths of submergence of 2.68 and 4.68. Measured wave forces in regular and irregular waves are then used to derive drag (C_D) and inertia coefficients (C_M). The analysis show that at very low KC numbers the inertia coefficients for all cylinders approached the potential flow values for both horizontal and vertical forces. The drag coefficients at low KC numbers exhibited large values and they decreased sharply with increase in KC number. For the square cylinder, where relatively a large KC number is obtained compared to other cylinders, inertia coefficients reached minimum values in the range of KC of about 3–4 and increased thereafter. In this range, C_M values are about 50% or so, smaller than the same at KC close to zero. The results of the experiments reveal that aspect ratio has large influence on hydrodynamic coefficients.     

Drag force on a vegetation field due to long-crested and short-crested nonlinear random waves

This paper provides a practical method for estimating the drag force on a vegetation field exposed to long-crested (2D) and short-crested (3D) nonlinear random waves. This is achieved by using a simple drag formula together with an empirical drag coefficient given by Mendez et al. (1999), in conjunction with a stochastic approach. Here the waves are assumed to be a stationary narrow-band random process. Effects of nonlinear waves are included by adopting the Forristall (2000) wave crest height distribution representing both 2D and 3D random waves.     

Bilge keel loads and hull pressures created by bilge keels fitted to a rotating cylinder

This paper presents bilge keel loads and hull pressure measurements carried out on a rotating cylinder in a free surface water basin. A flat plate bilge keel and one more complex shaped bilge keel were studied to investigate the geometry effect. The draft of the cylinder was varied to study the effect of the vicinity of the free surface on the bilge keel loads and hull pressures. The rotation axis of the cylinder was fixed to define a pure roll experiment (one degree of freedom).The cylinder was subject to forced oscillations of varying amplitude leading to a KC range of 0.3–16. Using Fourier analysis the first three harmonic coefficients representing the normal bilge keel load were derived. The first harmonic drag and inertia coefficients are in good agreement to existing experimental data obtained for wall bounded flat plates fitted in a U-shaped water tunnel as reported by Sarpkaya and O’Keefe (1996). New insight is gained by the fact that the addition of higher harmonic contributions is essential to capture the time varying bilge keel normal force.The pressure measurements next to the bilge keel are compared to measurements reported by Ikeda et al. (1979). Similar findings are obtained, showing that the pressure on the hull in front of the moving bilge keel is KC independent while the vortex system in the wake of the bilge keel leads to KC dependent hull pressure distributions. The hull pressure jump over the bilge keel correlates well to the force coefficient on the bilge keel. The complex nature of the vortex induced hull pressures is manifested. The empirically derived hull pressure distribution by Ikeda et al. (1979) for the time instant of maximum velocity is shown to correlate reasonably well to the measured data with some conservatism in the absolute value.Although a cylinder is very different from a ship-shaped section, the experiments provide essential insight into the physics associated with roll damping and into the factors that should be included in a roll damping prediction method.     

An experimental investigation of the characteristics of a cylinder interacting with waves and flow in the dominant-load regime

We describe in this paper the experimental investigations of the interaction of a bottom-pivoted vertical cylinder with water waves and flow, to determine the dominant-load-regime map by application of response step functions and response RAO. A rigid circular cylindrical mass-damper-spring oscillator system is investigated in regular waves and uniform flow to determine the response characteristics in the frequency domain. Interaction with waves dominates in the high frequency range f* = f_osc/ω_v = 0.862–1.547, with magnitude in the range of 0.1 rad. On the other hand, interaction with flow dominates at lower frequency range, f* = 0.442–0.862, with magnitude in the range of 0.01 rad. These are caused by the non-overlap peak positions of the magnitude response in waves and flow due to the change in added mass of the cylinder moving in different types of fluid loads. The frequency f* = 0.862 is the point where the dominant factors are transferred. The location of separation points determines the pressure distribution to induce the added mass changed. Separation positions determine the magnitude response, but do not determine the configuration of response RAO. That allows to enhance or reduce the magnitude response of the cylinder by taking advantage of the dominant-load-regime map in the frequency domain.     

On the radiation and diffraction of water waves by a rectangular structure with a sidewall

A radiation and diffraction boundary value problem is investigated. It arises from the interaction of linear water waves with a freely floating rectangular structure in a semi-infinite fluid domain of finite water depth with the leeward boundary being a vertical wall. Analytical expressions for the radiated potentials and the diffracted potential are obtained by use of the method of separation of variables and the eigenfunction expansion method. The added masses and damping coefficients for the structure heaving, swaying and rolling in calm water are obtained by use of the corresponding radiated potentials and the wave excitation forces are calculated by use of the diffracted potential. To verify the correctness of the method, a boundary element method is used. A comparison of the analytical results with those obtained by the boundary element method is made and good agreement is achieved, which shows that the analytical expressions for the radiated and diffracted potentials are correct. By use of the present analytical solution, the added mass, damping coefficients, wave excitation force, together with the hydrodynamic effects of the draft, width of the structure and the clearance between the structure and the sidewall are also investigated.     

Radiation and diffraction of linear water waves by an infinitely long submerged rectangular structure parallel to a vertical wall

The radiation and the diffraction of linear water waves by an infinitely long floating rectangular structure submerged in water of finite depth with leeward boundary being a vertical wall are analyzed in this paper by using the method of separation of variables. Analytical expressions for the radiated and diffracted potentials are derived as infinite series with unknown coefficients determined by the eigenfunction expansion matching method. The expressions for wave forces and hydrodynamic coefficients are given. A comparison is made between the results obtained by the present analytical solution and those obtained by the boundary element method. By using the present analytical solution, the hydrodynamic influences of the submergence, the width, the thickness of the structure, and the distance between the structure and the wall on the wave forces and hydrodynamic coefficients are discussed in detail.