Lars Bergdahl

Frequency-domain dynamic analysis of cables

A linear, frequency-domain, dynamic method is introduced to calculate large motions of slender structures such as towing and mooring cables, and flexible risers. The viscous, drag damping is linearized at element level by calculating linearized equivalent damping coefficients through iteration. In the introduced method the work done by the motion of the cable in the time domain is equated with that done in the frequency domain. The linearized, frequency-domain results are compared with results from nonlinear simulations for a towing cable, a mooring line and a lazy-wave riser. The influences of excitation frequency and excitation amplitude are considered.

Influence of current and seabed friction on mooring cable response: comparison between time-domain and frequency-domain analysis

For a single mooring cable, the effect of current and seabed friction on mooring-cable tension and energy dissipation are studied in both the time domain and the frequency domain. In the time domain, all nonlinearities can be taken into account. In the frequency domain, the nonlinear drag forces can be linearized either by a direct integration method or by statistical linearization techniques; for sea-floor effects, a simple lumped stiffness model and the statistical linearization method based on friction-controlled slip are combined. Two example structures, one flexible riser and one deep water mooring, are analysed. The time-domain and frequency-domain results compare well. The findings of the effects of current and friction on mooring-cable responses are discussed, they show that the linearized frequency-domain solution can produce satisfactory results.

Measurement and three-dimensional simulation of flow in a rectangular detention tank

There are two main ways to obtain better knowledge of the hydraulics of ponds, namely measurements and simulations. In this study, the applicability of using three-dimensional simulations as an engineering tool in stormwater pond design was investigated. To do this, three-dimensional simulations were compared with measurements of flow pattern and residence time in a large physical model of a detention tank (13 × 9 × 1 m). The agreement between measurements and simulations concerning both flow pattern and residence time distribution curves was found to be good for high flow rates.

Extreme mooring cable tensions due to wave-frequency excitations

The mooring cables of floating platforms respond non-linearly to the fairlead motions. Even though the wave-frequency excitation can be assumed to be a Gaussian process, the cable tension generally is not. Industry regulations prescribe calculation of maximum wave-frequency cable tension to obtain the total design value. However, time-domain calculations show that various realised time records of excitation with the same spectrum can result in big differences in simulated maximum cable tensions. Therefore, it is necessary to make many simulations or to perform statistical analysis on tension-time history. In this paper, the cable tension-time histories are determined by nonlinear time-domain dynamic simulation, and then the order statistic theory is applied to determine the expectation of maximum cable tension (extreme tension) corresponding to a specified time period. By doing this, it is shown that only one time-domain cable dynamic analysis plus statistical treatment are necessary to obtain a proper design value, instead of several simulations. The extreme values predicted in this way are also compared with those from the Hermite moment-based method. Major parameters such as cable slackness, current, excitation amplitudes etc. are varied to study their effects on the asymptotic distribution model and extreme values. The proposed procedures could be applied to other similar problems. Research on the extreme values for combined wave- and low-frequency excitations are continued.

On combination formulae for the extremes of wave-frequency and low-frequency responses

One special feature in moored floating platforms is the co-existence of the first-order wave-frequency (WF) response and the second-order low-frequency (LF) resonant response. Non-linear properties inherent in moored floating platforms cause the platform motions and mooring cable tensions to be non-Gaussian (not normal) distributed, both for the WF and for the LF components. As the LF and the WF components are not independent, it is important and necessary to find a simple, reliable and yet physically sound technique to estimate their combination. In this paper, on the basis of some model test results, different combination formulae are compared and a formula considering WF and LF correlation effects is suggested. A simple approach is also proposed to estimate the correlation factor.

Setting Up a Numerical Model of a DAF Tank: Turbulence, Geometry, and Bubble Size

This paper discusses the modeling framework and identifies a number of parameters relevant when setting up a computational fluid dynamics simulation of a dissolved air flotation (DAF) tank. The selection of a turbulence model, the choice between performing two-dimensional (2D) or three-dimensional (3D) simulations, the effects of the design of the flow geometry and the influence of the size of the air bubbles are addressed in the paper. The two-phase flow of air and water is solved in the Eulerian-Lagrangian frame of reference. The realizable k- model with nonequilibrium wall functions is suggested as a compromise between a need to effectively resolve the flow and the cost of the simulations. There is a discussion on the conditions for which the steady-state simulations are appropriate. We demonstrate that a steady 2D model can simulate a stratified flow pattern. Our results show that 2D models require adjustments in geometry (e.g., substitution of the outlet pipes to an outlet distributed over the total width of the tank) and in the parameters governing the flow in order to account for the true 3D nature of some of the flow patterns. In addition, we show that the bubble size has a larger influence on the flow in the separation zone than in the contact zone.

The Effect of Wind and Wave Misalignment on the Response of a Wind Turbine at Bockstigen

The aim of this work is to evaluate data from the offshore wind farm Bockstigen in order to study the effect of directional spreading of waves and wind wave misalignment on the response of the structure. The development of offshore wind energy has led to wind farms at sites with water depths ranging from approximately 6 to 30 m. The change of location from land to sea changes the design requirements of wind energy converters. In addition to wind loads, the wave load on the structure has to be taken into account. Since a wind turbine is highly damped in the inline direction as compared to the cross-wise direction, the effect of directional spreading of waves on the response is studied. Depending on the dynamics of the structure the crosswise force could give a larger response than the corresponding inline force. In this study the influence of the directional spreading of the waves on the response is not clear, however the effect of wind and wave misalignment is clear.

Extreme Non-Linear Wave Forces on a Monopile in Shallow Water

A phase averaging wave model (SWAN) is used to transform offshore sea states to the near to shore site of an offshore wind energy converter. The supporting structure of the wind turbine consists of a cylindrical monopile, and the wave forces and resulting base moments on it are calculated by Morison’s equation integrating from the bottom to the instantaneous free surface. For that purpose the wave-motion in the time domain at the monopile is realized by a second-order random wave model.Copyright

Coupled BEM/hp-FEM Modelling of Moored Floaters

A coupling between a dynamic mooring solver based on high-order finite element techniques (MooDy) and a radiation-diffraction based hydrodynamic solver (WEC-Sim) is presented. The high-order scheme gives fast convergence resulting in high-resolution simulations at a lower computational cost. The model is compared against a lumped mass mooring code (MoorDyn) that has an existing coupling to WEC-Sim. The two models are compared for a standard test case and the results are similar, giving confidence in the new WEC-Sim-MooDy coupling. Finally, the coupled model is validated using experimental data of a spread moored cylinder with good agreement.

Experimental and numerical investigation of a taut-moored wave energy converter—a validation of simulated buoy motions

This study presents an experimental and numerical investigation of a taut-moored wave energy converter system with a point-absorber type of wave energy converter. The wave energy converter system consists of a buoy, a unique three-leg two-segment mooring system with submerged floaters, and a power take-off system designed for the current experiment as a heave plate. The main objective of the study is to validate a numerical simulation model against experiments carried out in an ocean basin laboratory. Two physical models in model scales 1:20 and 1:36 were built and tested. The detailed experimental testing programme encompasses tests of mooring system stiffness, decay tests, and different sea state conditions for ocean current, regular, and irregular waves. A numerical model in the model scale 1:20 was developed to simulate coupled hydrodynamic and structural response analyses of the wave energy converter system, primarily using potential flow theory, boundary element method, finite element method, and the Morison equation. Several numerical simulations are presented for each part of the experimental testing programme. Results for the wave energy converter buoy motions under operational conditions from the experiments and the numerical simulations were compared. This study shows that the simulation model can satisfactorily predict the dynamic motion responses of the wave energy converter system at non-resonant conditions, while at resonant conditions additional calibration is needed to capture the damping present during the experiment. A discussion on simulation model calibration with regard to linear and non-linear damping highlights the challenge to estimate these damping values if measurement data are not available.