Wave Drift Forces on Two Floating Bodies Arranged Side by Side

An innovative hydrodynamic theory and numerical model were developed to help improve the efficiency, accuracy, and convergence of the numerical prediction of wave drift forces on two side-by-side deepwater floating bodies. The wave drift forces were expressed by the double integration of source strength and the corresponding Green function on the body surface, which is consistent with the far field formula based on momentum conservation and sharing the advantage of near field calculations providing the drift force on each body. Numerical results were validated through comparing the general far field model and pressure integral model, as well as the middle field model developed usin^z the software HydroStar.

SECOND-ORDER DRIFT FORCES AND MOMENTS BETWEEN TWO SUBMERGED BODIES IN WAVES ON 3D METHOD

Two near field methods, namely the integral method and differential method, were presented for giving second order mean drift forces and moments between two fixed submerged bodies in regular waves. For the integral method, with a series of mathematical manipulations, second order drift forces and moments could be easily expressed by distributed sources which could be calculated by source distribution techniques with the assumption that the amplitude of ship motions are small on the basis of the linear 3D frequency theory. For the differential method, drift forces and moments could be expressed by the derivative of velocity potential with respect to space coordinate. Because two bodies would behave as a single body while the clearance is very large, the numerical results of one sphere in such case were given and compared with analytical results of a single sphere which does not involve the effect of free surface. When submerged depth becomes enough large, a good agreement can be reached. Then the integral method was used to predict the second order drift forces and moments of two submerged spheres and spheroids with a small lateral separation distance in waves compared with the numerical results obtained by the differential method and they agree well. By comparison, it indicates the interaction effects between two submerged bodies have a profound influence on the drift forces and moments. In this paper, the forward speed effect on submerged spheres was also considered.

Using a Time-domain Higher-order Boundary Element Method to Simulate Wave and Current Diffraction from a 3-D Body

To study wave-current actions on 3-D bodies a time-domain numerical model was established using a higher-order boundary element method(HOBEM).By assuming small flow velocities,the velocity potential could be expressed for linear and higher order components by perturbation expansion.A 4th-order Runge-Kutta method was applied for time marching.An artificial damping layer was adopted at the outer zone of the free surface mesh to dissipate scattering waves.Validation of the numerical method was carried out on run-up,wave exciting forces,and mean drift forces for wave-currents acting on a bottom-mounted vertical cylinder.The results were in close agreement with the results of a frequency-domain method and a published time-domain method.The model was then applied to compute wave-current forces and run-up on a Seastar mini tension-leg platform.

HYDRODYNAMIC INTERACTION BETWEEN TWO VERTICALCYLINDERS IN WATER WAVES

The hydrodynamic interaction between two vertical cylinders in water waves is investigated based on the linearized potential flow theory. One of the two cylinders is fixed at the bottom while the other is articulated at the bottom and oscillates with small amplitudes in the direction of the incident wave. Both the diffracted wave and the radiation wave are studied in the present paper. A simple analytical expression for the velocity potential on the surface of each cylinder is obtained by means of Graf's addition theorem. The wave-excited forces and moments on the cylinders, the added masses and the radiation damping coefficients of the oscillating cylinder are all expressed explicitly in series form. The coefficients of the series are determined by solving algebraic equations. Several numerical examples are given to illustrate the effects of various parameters, such as the separation distance, the relative size of the cylinders, and the incident angle, on the first-order and steady second-order forces, the added masses and radiation-damping coefficients as well as the response of the oscillating cylinder.