Mooring systems with submerged buoys: influence of buoy geometry and modelling fidelity

Mooring systems often make use of submerged buoys (SBs) in order to make the moorings compliant. In this paper we present the dynamic effects of changing the buoy geometry or the buoy model fidelity on the mooring system response. Three cylindrical SBs with increasing slenderness (height/diameter) are studied for a mooring leg with two polyester ropes and a SB. The results show a large impact of SB geometry on the mooring dynamics. A larger height/diameter ratio (with preserved mass and buoyancy) is shown to be beneficial as it gives both smaller tension force magnitudes and, more importantly, avoids slack-snap occurrence in the upper cable. We further present a comparison between four numerical methods for SB dynamics: (i) a high-fidelity model using computational fluid dynamics (CFD); (ii) the Morison equation with slender body drag force approximation using numerical quadrature; (iii) the Morison equation with an independent evaluation of the fluid drag due to translation and rotation; and (iv) a translating Morison model which simulates a vertical cylinder in three degrees of freedom with no rotation. All methods are used together with a high-order finite element mooring dynamics solver. The results show that the translating method is inadequate to model this mooring configuration. The remaining three methods agree moderately well, but the Morison formulations give larger motions and higher tensions compared to the CFD results. We show that the quadrature drag model is better suited to model the drag moment on SBs than the independent model, and that the improvement increases with increasing slenderness of the buoy. The uncertainty, sensitivity and importance of the hydrodynamic coefficients of the buoy are discussed and examined by a regression analysis from the CFD data

Influence of bending stiffness on snap loads in marine cables: a study using a high-order discontinuous Galerkin method

Marine cables are primarily designed to support axial loads. The effect of bending stiffness on the cable response is therefore often neglected in numerical analysis. However, in low-tension applications such as umbilical modelling of ROVs or during slack events, the bending forces may affect the slack regime dynamics of the cable. In this paper, we present the implementation of bending stiffness as a rotation-free, nested local Discontinuous Galerkin (DG) method into an existing Lax–Friedrichs-type solver for cable dynamics based on an hp-adaptive DG method. Numerical verification shows exponential convergence of order P and P + 1 for odd and even polynomial orders, respectively. Validation of a swinging cable shows good comparison with experimental data, and the importance of bending stiffness is demonstrated. Snap load events in a deep water tether are compared with field-test data. The bending forces affect the low-tension response for shorter lengths of tether (200–500 m), which results in an increasing snap load magnitude for increasing bending stiffness. It is shown that the nested LDG method works well for computing bending effects in marine cables

High-order mooring simulations for increased accuracy in wave energy applications

The prevailing simulation technique for floating wave energy converters (WECs) is to use the linear hydrodynamics in convolution form to solve for the motion of the floating structure. This allows for very fast time domain simulations with the possibility to include non-linear reaction forces from e.g. moorings and power take off (PTO). Although its accuracy for very large motion amplitudes is debated (Yu and Li 2015, Palm 2015), it is the best method available to make long-term simulations of WEC response. Brown and Mavrakos (1999) showed a big difference in mooring response depending on how the mooring cables of marine structures where modeled. As WECs are subjected to large motions in relatively shallow water, the differences between different methods are pronounced compared to traditional oil and gas structures, and the uncertainty in model choice is still to be properly quantified. We present a coupling between the open source code WECSim (NREL), and a finite element code for mooring cable dynamics that specializes in accurately capturing snap loads. The in-house mooring model is based on the discontinuous Galerkin method and provides very low numerical diffusion of load propagation. We also present a comparison between our mooring model and using the native, lumped mass mooring model of WECSim, which is a standard method for mooring dynamics. The effect of changing mooring model is evaluated in terms of structural WEC response, peak, mooring load and its potential impact on the fatigue damage

INVESTIGATION OF NUMERICAL SCHEMES IN AIR CAVITY COMPUTATIONS

Air cavity and air chamber concepts have been proven to be an efficient way for drag reduction in low-speed ships. Series of experiments were conducted in the SSPA cavitation tunnel to simulate the working conditions of an air filled cavity under the hull of a ship. In this paper, study is extended with a numerical validation using a CFD Open Source solver, OpenFOAM (OF). Volume of fluid (VOF) approach, which uses phase volume fraction (alpha) is used to compute the incompressible two-phase viscous flow. The influence of different numerical methodologies on the advection of "alpha" is studied. Different schemes from diffusive first-order to higher order TVD (Total Variation Dimensioning) schemes like SUPERBEE are tested. Results are also drawn from counter-gradient convective flux implementation in OF VOF approach. Conclusions are drawn from the wave profile, wave sloshing pressure force and viscous force. It was observed that, as more compressive interface capturing methods were used, the aft force was better predicted but distorts the wave profile and under predicts the beach plate force

A Spectral Element Method for Nonlinear and Dispersive Water Waves

The use of flexible mesh discretisation methods are im-portant for simulation of nonlinear wave-structure inter-actions in offshore and marine settings such as harbour and coastal areas. For real applications, development of efficient models for wave propagation based on un-structured discretisation methods is of key interest. We present a high-order general-purpose three-dimensional numerical model solving fully nonlinear and dispersive potential flow equations with a free surface. Figure 1: Snapshot of scaled free surface showing diffraction and refraction patterns in the free surface. Governing equations Let both Ω ⊂ Rd (d = 2, 3) and Ω ′ ⊂ Rd−1 be bounded, connected domains with piecewise smooth boundaries Γ and Γ′, respectively. Let T: t ≥ 0 be the time domain. Introduce the free surface boundary ΓFS ⊂ Γ and the bottom boundary Γb ⊂ Γ. The mathematical problem is to find a scalar velocity potential function φ(x, z, t): Ω × T → R and to determine the evolution of the free surface elevation η(x, t) : Ω ′ × T → R. The Eulerian description of the unsteady kinematic and a dynamic free surface boundary conditions is ex-pressed in the Zakharov form. In Ω ′ × T, find η, φ̃ ∂tη = −∇η · ∇φ̃+ w̃(1 +∇η · ∇η) ∂tφ ̃ = −gη −

Dynamically Scaled Model Experiment of a Mooring Cable

The dynamic response of mooring cables for marine structures is scale-dependent, and perfect dynamic similitude between full-scale prototypes and small-scale physical model tests is difficult to achieve. The best possible scaling is here sought by means of a specific set of dimensionless parameters, and the model accuracy is also evaluated by two alternative sets of dimensionless parameters. A special feature of the presented experiment is that a chain was scaled to have correct propagation celerity for longitudinal elastic waves, thus providing perfect geometrical and dynamic scaling in vacuum, which is unique. The scaling error due to incorrect Reynolds number seemed to be of minor importance. The 33 m experimental chain could then be considered a scaled 76 mm stud chain with the length 1240 m, i.e., at the length scale of 1:37.6. Due to the correct elastic scale, the physical model was able to reproduce the effect of snatch loads giving rise to tensional shock waves propagating along the cable. The results from the experiment were used to validate the newly developed cable-dynamics code, MooDy, which utilises a discontinuous Galerkin FEM formulation. The validation of MooDy proved to be successful for the presented experiments. The experimental data is made available here for validation of other numerical codes by publishing digitised time series of two of the experiments

Uncertainty quantification of the dynamics of a wave energy converter

Since time-domain simulations of wave energy converters are computationally expensive, how can we analyse their dynamics and test wide ranges of design variables, without simplifying the physics involved? One possible solution is the use of General Polynomial Chaos (gPC). GPC provides computationally efficient surrogate models for partial differential equation based models, which are particularly useful for sensitivity analysis and uncertainty quantifica- tion. We demonstrate the application of gPC to study the dynamics of a wave energy converter in an operational sea-state, when there is uncertainty in the values of the stiffness and damping coefficient of the power take-off

Facilitating Large-Amplitude Motions of Wave Energy Converters in OpenFOAM by a modified Mesh Morphing Approach

High-fidelity simulations using computational fluid dynamics (CFD) for wave-body interaction are becoming increasingly common and important for wave energy converter (WEC) design. The open source finite volume toolbox OpenFOAM is one of the most frequently used platforms for wave energy. There are currently two ways to account for moving bodies in OpenFOAM: (i) mesh morphing, where the mesh deforms around the body; and (ii) an overset mesh method where a separate body mesh moves on top of a background mesh. Mesh morphing is computationally efficient but may introduce highly deformed cells for combinations of large translational and rotational motions. The overset method allows for arbitrarily large body motions and retains the quality of the mesh. However, it comes with a substantial increase in computational cost and possible loss of energy conservation due to the interpolation. In this paper we present a straightforward extension of the spherical linear interpolation (SLERP) based mesh morphing algorithm that increase the stability range of the method. The mesh deformation is allowed to be interpolated independently for different modes of motion, which facilitates tailored mesh motion simulations. The paper details the implementation of the method and evaluates its performance with computational examples of a cylinder with a moonpool. The examples show that the modified mesh morphing approach handles large motions well and provides a cost effective alternative to overset mesh for survival conditions