Numerical Study of Effects of Complex Topography on Surface-Piercing Wave-Body Interactions

In this paper, wave-body interactions under the effects of complex topography are investigated numerically by a two-phase incompressible Reynolds-Averaged Navier-Stokes(RANS) solver in OpenFOAM. A submerged bottom-standing structure is distributed below the floating body, and the effects of the water depth and top width of the submerged structure on wave-body interactions are studied. The results show that the submerged structure can affect wave loads and roll motion. The vertical force can be amplified on the fixed body when the water depth of the submerged structure is smaller than half of the water depth of the body. The top width significantly affects the vertical force when the top width is smaller than the incident wave length and larger than the body width. For the free-rolling body, roll amplitude can be increased when the ratio of the incident wave length to the water depth of the submerged structure is large enough. On the resonance condition, roll amplitude is slightly reduced by the submerged structure. The effects of the top width on roll amplitude are remarkable when special conditions are fulfilled.

WAVE-BODY INTERACTIONS FOR A SURFACE-PIERCING BODY IN WATER OF FINITE DEPTH

Nonlinear wave-body interactions for a stationary surface-piercing body in water of finite depth with fiat and sloping bottoms are simulated in a two-dimensional numerical wave tank, which is constructed mainly based on the spatially averaged Navier-Stokes equations with the k- ε model for simulating the turbulence. The equations are discretized based on the finite volume method and the scheme of the pressure implicit splitting of operators is employed to solve the Navier-Stokes equations. By using the force time histories, the mean and higher-harmonic force components are calculated. The computational results are shown to be in good agreement with experimental and numerical results of other researchers. Then, the horizontal force, the vertical force and the moment on the surface-piercing body under nonlinear regular waves with flat and sloping bottoms are obtained. The results indicate that the bottom topographies have a significant influence on the wave loads on the surface-piercing body.

Desingularized boundary integral equations and their applications in wave dynamics and wave-body interaction problems

Over the past 30 years or so,desingularized boundary integral equations(DBIEs)have been used to study water wave dynamics and body motion dynamics.Within the potential flow modeling,unlike conventional boundary integral methods,a DBIE separates the integration surface and the control(collocation)surface,resulting in a BIE with non-singular kernels.The desingularization allows simpler and faster numerical evaluation of the boundary integrals,and consequently faster numerical solutions.In this paper,derivations of different forms of DBIEs are given and the fundamental aspects and advantages of the DBIEs are reviewed and discussed.Numerical examples of applications of DBIEs in wave dynamics and body motion dynamics are given and the outlook of future development of the desingularized methods is discussed.

Application of the generalized body-fixed coordinate system for the wave-body interaction problem of a small-depth elastic structure in head seas

The body-fixed coordinate system is applied to the wave-body interaction problem of a small-depth elastic structure which has both rigid and elastic body motions in head waves.In the weakly non-linear assumption,the perturbation scheme is used and the expansion is conducted up to second-order to consider several non-linear quantities.To solve the boundary value problem,linearization is carried out based not on inertial coordinate but on body-fixed coordinate which could be accelerated by a motion of a body.At first,the main feature of the application of body-fixed coordinate system for a seakeeping problem is briefly described.After that the transformation of a coordinate system is extended to consider an elastic body motion and several physical variables are re-described in the generalized mode.It has been found that the deformation gradient could be used for the transformation of a coordinate system if several conditions are satisfied.Provided there are only vertical bending in elastic modes and the structure has relatively small depth,these conditions are generally satisfied.To calculate an elastic motion of a body,the generalized mode method is adopted and the mode shape is obtained by solving eigen-value problem of dynamic beam equation.In the boundary condition of the body-fixed coordinate system,the motion effect reflected to free-surface boundary is considered by extrapolating each mode shape to the horizontal direction from a body.At last,simple numerical tests are implemented as a validation process.The second-order hydrodynamic force of a freely floating hemisphere is first calculated in zero forward speed condition.Next,motion and added resistance of a ship with forward speed are considered at different flexibility to confirm the effect of an elastic body motion in body-fixed coordinate system.

Numerical Wave Flume Study on Wave Motion Around Submerged Plates

Nonlinear interaction between surface waves and a submerged horizontal plate is investigated in the absorbed numerical wave flume developed based on the volume of fluid (VOF) method. The governing equations of the numerical model are the continuity equation and the Reynolds-Averaged Navier-Stokes (RANS) equations with the k-ε turbulence equations. Incident waves are generated by an absorbing wave-maker that eliminates the waves reflected from structures. Results are obtained for a range of parameters, with consideration of the condition under which the reflection coefficient becomes maximal and the transmission coefficient minimal. Wave breaking over the plate, vortex shedding downwave, and pulsating flow below the plate are observed. Time-averaged hydrodynamic force reveals a negative drift force. All these characteristics provide a reference for construction of submerged plate breakwaters.

Development of Cartesian grid method for simulation of violent ship-wave interactions

We present a Cartesian grid method for numerical simulation of strongly nonlinear phenomena of ship-wave interactions. The Constraint Interpolation Profile （CIP） method is applied to the flow solver, which can efficiently increase the discretization accuracy on the moving boundaries for the Cartesian grid method. Tangent of Hyperbola for Interface Capturing （THINC） is imple- mented as an interface capturing scheme for free surface calculation. An improved immersed boundary method is developed to treat moving bodies with complex-shaped geometries. In this paper, the main features and some recent improvements of the Cartesian grid method are described and several numerical simulation results are presented to discuss its performance.

A 3-D SPH model for simulating water flooding of a damaged floating structure

With the quasi-static analysis method, the terminal floating state of a damaged ship is usually evaluated for the risk assessment. But this is not enough since the ship has the possibility to lose its stability during the transient flooding process. Therefore, an enhanced smoothed particle hydrodynamics（SPH） model is applied in this paper to investigate the response of a simplified cabin model under the condition of the transient water flooding. The enhanced SPH model is presented firstly including the governing equations, the diffusive terms, the boundary implementations and then an algorithm regarding the coupling motions of six degrees of freedom（6-DOF） between the structure and the fluid is described. In the numerical results, a non-damaged cabin floating under the rest condition is simulated. It is shown that a stable floating state can be reached and maintained by using the present SPH scheme. After that, three-dimensional（3-D） test cases of the damaged cabin with a hole at different locations are simulated. A series of model tests are also carried out for the validation. Fairly good agreements are achieved between the numerical results and the experimental data. Relevant conclusions are drawn with respect to the mechanism of the responses of the damaged cabin model under water flooding conditions.