Numerical Analysis of Second-Order Mean Wave Forces by a Stabilized Higher Order Boundary Element Method

A stabilized Higher-Order Boundary Element Method (HOBEM) based on cubic shape functions is presented to solve the linear wave-structure interaction with the presence of steady or slowly varying velocities. The m-terms which involves second derivatives of local steady flow are difficult to calculate accurately on structure surfaces with high curvatures. They are also not integrable at the sharp corners. A formulation of the Boundary Value Problem (BVP) in a body-fixed coordinate system is thus adopted, which avoids the calculation of the m-terms. The use of body-fixed coordinate system also avoid the inconsistency in the traditional perturbation method when 2nd order slowly-vary motions are larger than the linear motions. The stabilized numerical method presented in this paper is based on streamline integration and biased differencing scheme along the streamlines. The presence of convective terms in the kinematic and dynamic free surface conditions will lead to instable solution if the explicit method is used. Thus a fully implicit scheme is used in this paper for the time integration of kinematic and dynamic free surface conditions. In an implicit scheme, solution of an additional matrix equation is normally required due to the fact that the presence of convective terms are approximated using the variables at current time step rather than the previous time steps only. A method that avoids solving such matrix equation is presented in this paper, which will reduce the computational efforts in the implicit method. The methodology is applicable on unstructured meshes. It can also be used in general second order wave-structure interaction analysis with presence of steady or slowly-varying velocities.

An Improved Body-Exact Method to Predict Large Amplitude Ship Roll Responses

Accurate prediction of the roll response is of significant practical relevance not only for ships but also ship type offshore structures such as FPSOs, FLNGs and FSRUs. This paper presents a new body-exact scheme that is introduced into a nonlinear direct time-domain based strip theory formulation to study the roll response of a vessel subjected to moderately large amplitude incident waves. The free surface boundary conditions are transferred onto a representative incident wave surface at each station. The body boundary condition is satisfied on the instantaneous wetted surface of the body below this surface. This new scheme allows capturing nonlinear higher order fluid loads arising from the radiated and wave diffraction components. The Froude-Krylov and hydrostatic loads are computed on the intersection surface of the exact body position and incident wave field. The key advantage of the methodology is that it improves prediction of nonlinear hydrodynamic loads while keeping the additional computational cost small. Physical model tests have been carried out to validate the computational model. Fairly good agreement is seen. Comparisons of the force components with fully linear and body-nonlinear models help in bringing out the improvements due to the new formulation.

Wave Diffraction on Arrays of Vertical Truncated Cylindrical Bodies

Offshore Wave Energy Converter (WEC) farms are widely deployed as regards the individual isolated devices aiming at maximum wave energy absorption and facilitating installation and power transmission. This paper summarizes the theory behind the hydrodynamic interactions of diffracted waves by a large array of vertical cylinders. The latter exhibits some remarkable hydrodynamic interference effects — near resonant modes — in waves causing large loads in adjacent elements of the array. Numerical results concerning the exciting wave loads for a variety of different array configurations of truncated and bottomless cylinders are presented and the free surface elevation around the elements of the array is evaluated pointing out the near trapped modes.

Hydrodynamics Around a Deep-Draft Semi-Submersible With Various Corner Shapes

A numerical study on flow over a stationary deep-draft semi-submersible (DDS) with various corner shapes was carried out to investigate the corner shape effects on the overall hydrodynamics. Three models based on a typical DDS design with different corner shapes were numerically investigated under 45° incidence. The present numerical model has been validated by an experimental test carried out in a circulating water channel. It is demonstrated that, as the corner shape design changed, the hydrodynamic characteristics alter drastically. In addition, the flow patterns were examined to reveal some insights of the fluid physics due to the changing of different corner shape designs. The detailed numerical results from the geometric study will provide a good guidance for future practical designs.

Modelling Turbulent Flow in Deformable Highly Porous Seabed and Structures

In this study, the fully-coupled and fully-dynamic Biot governing equations in the open-source geotechFoam solver are extended to account for pore fluid viscous stresses. Additionally, turbulent pore fluid flow in deformable porous media is modeled by means of the conventional eddy viscosity concept without the need to resolve all turbulence scales. A new approach is presented to account for porous media resistance to flow (solid-to-fluid coupling) by means of an effective viscosity, which accounts for tortuosity, grain shape and local turbulences induced by flow through porous media. The new model is compared to an implemented extended Darcy-Forchheimer model in the Navier-Stokes equations, which accounts for laminar, transitional, turbulent and transient flow regimes. Further, to account for skeleton deformation, the porosity and other model parameters are updated with regard to strain of geomaterials. The presented model is calibrated by means of available results of physical experiments of unidirectional and oscillatory flows.

Performance of a Wave-Energy-Converter Array Operating Under Model-Predictive Control Based on a Convex Formulation

Economics decision drives the operation of ocean-wave energy converters (WEC) to be in a “farm mode”. Control strategy developed for a WEC array will be of high importance for improving the aggregate energy extraction efficiency of the whole system. Model-predictive control (MPC) has shown its strong potential in maximizing the energy output in devices with hard constraints on operation states and machinery inputs (See Ref. [1–3]). Computational demands for using MPC to control an array in real time can be prohibitive. In this paper, we formulate the MPC to control an array of heaving point absorbers, by recasting the optimization problem for energy extraction into a convex Quadratic Programming (QP) problem, the solution of which can be carried out very efficiently. Large slew rates are to be penalized, which can also guarantee the convexity of the QP and improve the computational efficiency for achieving the optimal solution. Constraints on both the states and the control input can be accommodated in this MPC method. Full hydro-dynamic interference effects among the WEC array components are taken into account using the theory developed in [4]. Demonstrative results of the application are presented for arrays of two, three, and four point absorbers operating at different incident-wave angles. Effects of the interacting waves on power performance of the array under the new MPC control are investigated, with simulations conducted in both regular and irregular seas. Heaving motions of individual devices at their optimal conditions are shown. Also presented is the reactive power required by the power takeoff (PTO) system of the array to achieve optimality. We are pleased to contribute this article in celebration of our collegiality with Professor Bernard Molin on the occasion of his honoring symposium.

Experimental Study of the Influence of the Pore Water Pressure Evolution and the Shear Band Formation on the Extraction Resistance of Submerged Anchor Plates

Floating offshore structures used to generate wind energy are founded on submerged foundations such as anchor plates. Their extraction resistance is of major importance during and at the end of the lifetime cycle of these offshore structures. During their lifetime cycle, the foundation is suspended to complex loading conditions due to waves, tidal currents and wind loads. To guarantee a stable structure, the extraction resistance of the anchor plates has to be known. At the end of the lifetime cycle of the offshore structures, the extraction resistance is mainly influencing the removal of the anchor plates. This resistance is a lot higher than the sum of its self-weight and hydrostatic and earth pressure acting on the structure. With initiation of a motion of the anchor plate, the volume underneath this structure is increased leading to negative pore water pressure until inflowing pore water is filling the newly created volume. In order to investigate this effect, an extensive experimental study at model scale with a displacement-driven extraction is performed. Pore pressure measurements are carried out at various locations in the soil body and underneath the plate. The soil movement is tracked with a high-speed camera to investigate the shear band formation with the particle image velocimetry method (PIV). The experiments will be conducted considering different packing densities of the soil body and at different extraction velocities to investigate their effect on the extraction resistance of anchor plates.

Hydrodynamic Interactions of the Truncated Porous Vertical Circular Cylinder With Water Waves

Wave diffraction-radiation by a porous body is investigated here. Linear potential flow theory is used and the associated Boundary Value Problem (BVP) is formulated in frequency domain within a linear porosity condition. First, a semi-analytical solution for a truncated porous circular cylinder is developed using the dedicated eigenfunction expansion method. Then the general case of wave diffraction-radiation by a porous body with an arbitrary shape is discussed and solved through Boundary Integral Equation Method (BIEM). The main goal of these developments is to adapt the existing diffraction-radiation code (HYDROSTAR) for that type of applications. Thus the present study of the porous cylinder consists a validation work of (BIEM) numerical implementation. Excellent agreement between analytical and numerical results is observed. Porosity influence on wave exciting forces, added mass and damping is also investigated.

Simulation of Working Posture of Deepwater Gravity Sampling Device Using OpenFOAM

Computational fluid dynamics (CFD) has been widely used in the field of marine engineering recent years. In this work, the free falling process and working posture of gravity sampler have been studied using OpenFOAM. The overset grids have been used to simulate the movement of the sampler in the flow field. Main works are as follows: (1) verifying the accuracy of the overset grid method; (2) establishing a numerical model using the Newmark method to analyze the responses of sampler vertical and slant drop; (3) investigating the relationship among the deflection angle, falling speed and sampling rate of sampler. Finally, the best fall distance of GPS-01 sampler has been recommended in combination with the falling velocity and the initial falling angle.

Numerical Study of Phase Change Influence on Wave Impact Loads in LNG Tanks on Floating Structures

Understanding the physics of sloshing wave impacts is necessary for the improvement of sloshing assessment methodology based on sloshing model tests, for LNG membrane tanks on floating structures. The phase change between natural gas and liquefied natural gas is one of the physical phenomena involved during a LNG wave impact but is not taken into account during sloshing model tests. In this paper, some recent numerical and analytical works on the influence of phase change are summarized and discussed. For the impact of an ideally shaped wave, phase change influences two different steps of the impact in different ways: during the gas escape phase, phase change leads to a higher impact velocity; for entrapped gas pockets, phase change causes a reduction of the pressure in the gas pocket. However, this influence is quantitatively small. The generalization to more realistic wave shapes (including e.g. liquid aeration) should be the focus of future works.