Carl Trygve Stansberg

Breaking Wave Kinematics and Resulting Slamming Pressures on a Vertical Column

A need has been identified to improve the knowledge about extreme slamming loads from breaking waves on vertical columns, such as offshore platforms and wind turbine foundations. Due to strongly nonlinear physical mechanisms and large statistical variability, more and improved experimental data are needed, as well as better qualified design procedures. In this paper, model test data and CFD simulations from a recent study with a fixed vertical column are compared and investigated in more detail. Selected individual extreme slamming events due to energetic breaking waves in 1:40 and 1:125 scaled model tests are presented and considered. Waves correspond approximately to extreme breaking wave occurrences in steep energetic sea states with 10-4 annual probability in the Norwegian sector.Slamming pressures on the column wall are measured in time and space by means of a 7 × 7 pressure sensor array covering 19m2 (full scale). Significant spatial variations are observed. When spatially averaged over the array, the observed highest pressures are typically in the range 1MPa–3MPa (full scale), while smaller measuring areas give higher values. This compares roughly to levels found from recent results in the literature; although exact comparison is difficult due to statistical uncertainty issues. Experiences obtained from parallel CFD and PIV activities are also compared to the experiments, from which free-surface particle velocities up to 25m/s (full scale) are estimated in the worst cases. Finally, a simple empirical formula for a slamming coefficient depending on the actual pressure integration area is suggested based on the results.Copyright

Second-Order Random Wave Kinematics and Resulting Loads on a Bottom-Fixed Slender Monopile

The importance of including second-order nonlinear random wave kinematics in the numerical prediction of drag-induced shear forces and moments, at various levels on a bottom-fixed slender monopile in 40m water depth, is investigated. A vertical circular cylinder of diameter 0.5m is considered, representing typical dimensions of members in jacket type foundations of offshore wind turbines. The focus is here on the wave loads only, and wind and a propeller are therefore not included in this study. In particular, the main focus is on the effects from second-order random wave kinematics on the structural quasi-static time-varying loads due to drag forces in heavy storm wave conditions. Comparisons are made to the traditional use of Airy waves with various ways of stretching.An in-house numerical FEM code developed for structural analysis, NIRWANA, is used for this study. Thus one purpose of the present work is also to verify the implementation of the second-order random waves in the code.The results show significant effects, especially in the wave zone. Extreme crests are around 15%–20% increased, free-surface extreme particle velocities increase by around 30%–40%, while the velocities at levels below MWL are, on the other hand, somewhat reduced. The resulting peak shear forces, and in particular the moments, are thereby increased by typically 50%–100% in the upper parts of the column. At the base the peak shear forces are comparable to the traditional methods, while moments are still somewhat higher. Another effect is the generation of more high-frequency load contributions, which may be important to address further with respect to natural frequencies of such towers.Copyright

Wave Drift Forces and Low Frequency Damping on the Exwave Semi-Submersible

The paper presents realistic horizontal wave drift force coefficients and low frequency damping coefficients for the Exwave semi-submersible under severe seastates. The analysis includes conditions with collinear waves and current. Model test data is used to identify the difference frequency wave exciting force coefficients based on a second order signal analysis technique. First, the slowly varying excitation is estimated from the relationship between the incoming wave and the low frequency motion using a linear oscillator. Then, the full quadratic transfer function (QTF) of the difference frequency wave exciting forces is defined from the relationship between the incoming waves and the second order force response. The process identifies also the linear low frequency damping. The paper presents results from cases selected from the EXWAVE JIP test matrix. The empirical wave drift coefficients are compared to potential flow predictions and to coefficients from a semi-empirical formula. The results show that the potential flow predictions largely underestimate the wave drift forces, especially at the low frequency range where severe seastates have most of the energy.

Wave Drift Forces and Low Frequency Damping on the Exwave FPSO

A method is followed in the present analysis to estimate realistic surge and sway wave drift force coefficients for the Exwave FPSO. Model test data is used to identify the difference frequency wave exciting force coefficients based on a second order signal analysis technique. First, the slowly varying excitation is estimated from the relationship between the incoming wave and the low frequency motion using a linear oscillator. Then, the full QTF of the difference frequency wave exciting forces is defined from the relationship between the incoming waves and the second order force response. The process identifies also the linearized low frequency damping. The paper presents results from a few cases selected from the Exwave JIP test matrix. Empirical mean wave drift coefficients are compared to potential flow predictions. It is shown that the latter underestimate the wave drift forces, especially at the lower frequency range where severe seastates have most of the energy. The sources for the discrepancies are discussed..

Effects of Wave-Current Interaction on Floating Bodies

Wave-current interaction effects may significantly influence the mean wave drift forces on a structure as well as the motion responses and wave elevation around the structure. Additionally, the drift force may be used to estimate the wave drift damping of a moored structure.A new numerical potential theory code for industry applications (MULDIF) has been recently developed, where the hydrodynamic interaction between waves and current of arbitrary direction with large volume structures is consistently included. The code also handles multiple bodies and finite water depth including wave-current interaction effects. The aim has been to create a robust and easy-to-use practical tool.Initial validation studies against model tests have been conducted. The numerical results show a strong heave-pitch coupling due to the presence of the current. Preliminary results for a semi-submersible show good agreement for the motions provided that the mooring used in the model tests are accounted for. The free surface elevation around the semi-submersible is presented in contour plots.Copyright

A Modified Linear Lagrangian Model for Irregular Long-Crested Waves

Wave crest height and steepness are crucial parameters for the design of ships and offshore structures. For irregular sea states, they are commonly predicted by using linear wave theory and a Eulerian description of the fluid motion. This theory only applies when the wave steepness is small and it fails to capture extreme wave events. Such linear solutions can also be extended by including second-order terms in order to provide more realistic wave properties. The paper describes a model for irregular long-crested waves that is based on a modified linear solution derived from a Lagrangian description of the fluid, i.e. by considering the motion of individual fluid particles. Lagrangian solutions have the advantage of showing realistic wave profiles with sharp crests and broad troughs already at the first order, whereas these features only appear at the second order when using the Eulerian approach. Still, a severe drawback with the former is that the mass conservation is not fulfilled exactly. The aim of the modification in the present Lagrangian model is to ensure that the mass conservation is always fulfilled in the solution. This is done by using the second-order residual in the continuity equation to lift up the fluid particles vertically. Comparative investigations of wave properties such as the crest height and the wave steepness are further carried out by making use of both numerical case studies and wave tank recordings. The wave models used in the comparisons include linear and second-order Eulerian solutions as well as the modified linear Lagrangian one.Copyright