Henrik Bredmose

Violent breaking wave impacts. Part 2: modelling the effect of air

When an ocean wave breaks against a steep-fronted breakwater, sea wall or a similar marine structure, its impact on the structure can be very violent. This paper describes the theoretical studies that, together with field and laboratory investigations, have been carried out in order to gain a better understanding of the processes involved. The waves approach towards a structure is modelled with classical irrotational flow to obtain the different types of impact profiles that may or may not lead to air entrapment. The subsequent impact is modelled with a novel compressible-flow model for a homogeneous mixture of incompressible liquid and ideal gas. This enables a numerical description of both trapped air pockets and the propagation of pressure shock waves through the aerated water. An exact Riemann solver is developed to permit a finite-volume solution to the flow model with smallest possible local error. The high pressures measured during wave impacts on a breakwater are reproduced and it is shown that trapped air can be compressed to a pressure of several atmospheres. Pressure shock waves, reflected off nearby surfaces such as the seabed, can lead to pressures comparable with those of the impact. Typical examples of pressure-time histories, force and impulse are presented and discussed in terms of their practical implications. The numerical model proposed is relevant for a variety of flows where air effects are important. Further applications, including extended studies of wave impacts, are discussed. 2009 Cambridge University Press.

Experimental investigation and numerical modelling of steep forced water waves

Steep forced water waves generated by moving a rectangular tank are investigated both experimentally and numerically. Our main focus is on energetic events generated by two different types of external forcing. Horizontal motions are arranged to give wave impact on the sidewall. Steep standing waves forced by vertical acceleration can result in spectacular breaking modes similar to, and more energetic than, those reported by Jiang, Perlin & Schultz (1998, hereinafter J98). Among them we find thin sheets derived from sharp-crested waves, (‘mode A’ of J98) and the ‘flat-topped’ crest or ‘table-top’ breaker (‘mode B’ of J98). We report here on experimental observations of ‘table-top’ breakers showing remarkably long periods of free fall motion. Previously such breakers have only been observed in numerical computations. Both types of breakers often thin as they fall to give thin vertical sheets of water whose downward motion ends in either a small depression and a continuing smooth surface, or air entrainment to appreciable depths. Experimental results are compared graphically with numerical results of two theoretical models. One is an extended set of Boussinesq equations following Wei et al. (1995), which are successful up to wave slopes of O (1). The other numerical comparison is with a fully nonlinear irrotational flow solver (Dold 1992) which can follow the waves to breaking.

Breaking Wave Impacts on Offshore Wind Turbine Foundations: Focused Wave Groups and CFD

Extreme wave loads from breaking waves on a monopile foundation are computed within a 3D CFD model. The wave impacts are obtained by application of focused wave groups. For a fixed position of the monopile, the focus location of the wave group is varied to produce impacts with front shapes that varies from early stages of breaking to broken waves. The CFD results for in-line force are compared to load estimates obtained from the Morison equation. The peak loads determined with this simple method are smaller than those of the CFD solution. The computational results appear to suggest that for the impacts of spilling breakers the peak force gets smaller the more developed the breaking is. This is in qualitative agreement with a finding from shallow water impacts on vertical walls: the strongest wave loads are associated with breakers that hit the structure with slightly overturning front. Extensions of the study are discussed.Copyright

A computational method for sharp interface advection

We devise a numerical method for passive advection of a surface, such as the interface between two incompressible fluids, across a computational mesh. The method is called isoAdvector, and is developed for general meshes consisting of arbitrary polyhedral cells. The algorithm is based on the volume of fluid (VOF) idea of calculating the volume of one of the fluids transported across the mesh faces during a time step. The novelty of the isoAdvector concept consists of two parts. First, we exploit an isosurface concept for modelling the interface inside cells in a geometric surface reconstruction step. Second, from the reconstructed surface, we model the motion of the face–interface intersection line for a general polygonal face to obtain the time evolution within a time step of the submerged face area. Integrating this submerged area over the time step leads to an accurate estimate for the total volume of fluid transported across the face. The method was tested on simple two-dimensional and three-dimensional interface advection problems on both structured and unstructured meshes. The results are very satisfactory in terms of volume conservation, boundedness, surface sharpness and efficiency. The isoAdvector method was implemented as an OpenFOAM® extension and is published as open source.

Vertical Wave Impacts on Offshore Wind Turbine Inspection Platforms

Breaking wave impacts on a monopile at 20 m depth are computed with a VOF (Volume Of Fluid) method. The impacting waves are generated by the second-order focused wave group technique, to obtain waves that break at the position of the monopile. The subsequent impact from the vertical run-up flow on a horizontal inspection platform is computed for five different platform levels. The computational results show details of monopile impact such as slamming pressures from the overturning wave front and the formation of run-up flow. The results show that vertical platform impacts can occur at 20 m water depth. The dependence of the vertical platform load to the platform level is discussed. Attention is given to the significant downward force that occur after the upward force associated with the vertical impact. The effect of the numerical resolution on the results is assessed. The position of wave overturning is found to be influenced by the grid resolution. For the lowest platform levels, the vertical impact is found to contribute to the peak values of in-line force and overturning moment.Copyright

Dynamic Excitation of Monopiles by Steep and Breaking Waves: Experimental and Numerical Study

An experiment with a flexible pile subjected to steep and breaking irregular waves has been conducted. The pile was constructed to represent a monopile wind turbine at scale 1:80. Two point masses were mounted on the pile to achieve the right scaled values for the first and second natural frequency. Emphasis is given to the observed impulsive excitation of the natural modes by steep and breaking waves. Additionally, springing and ringing-type continuous forcing of the first natural mode is seen for the moderately steep waves.The experiments were carried out at three depths and with two wave climates. The measured data for structural acceleration is analysed with respect to individual wave parameters. It is found that the largest accelerations occur for breaking waves.The measured wave field and structural response are reproduced numerically with a fully nonlinear potential flow solver for the undisturbed wave kinematics, combined with a finite element model with Morison-based forcing. A good overall reproduction of the wave field and structural response is achieved for two selected episodes. For some of the waves, however, the numerical response magnitude does not match the observed excitations. Ongoing work is therefore an investigation of breaking wave load models and their implementation into the present numerical frame work.© 2013 ASME

Field and Laboratory Measurement of Wave Impacts

An extensive program of ongoing field, laboratory, and numerical investigations into the characteristics of wave impacts is described and early results presented. Shock pressures are found to be highly localized, both spatially and temporally, able to propagate into cracks and, in freshwater at least, capable of reaching surprising intensities. Conventional scaling of 1:4 hydraulic model data implies that ocean waves approximately 4m high could generate heads in excess of 1000m. Attention is drawn to the probability that, in practice, such extreme pressures may be constrained by the acoustic (water hammer) limit. The parameter map (Allstop & Kortenhaus, 2001) used for predicting impacts is shown not to be entirely reliable and preliminary results of the numerical models are discussed.

FIELD AND LARGE SCALE MODEL TESTS OF WAVE IMPACT PRESSURE PROPAGATION INTO CRACKS

Within a large & full scale study on wave impact induced pressures on coastal structures (BWIMCOST) an investigation of impact pressure propagation into structure cracks and fissures was carried out. The mechanism, which is held responsible for localized damage to existing blockwork breakwaters, had previously been verified in small scale model tests and a numerical model had been developed. The current investigation is the first which describes the effect at full scale, with recorded pressures of up to 199 kPa found within the cracks. The experimental results are related to their possible impact on coastal structural integrity.

Effects From Fully Nonlinear Irregular Wave Forcing on the Fatigue Life of an Offshore Wind Turbine and its Monopile Foundation

The effect from fully nonlinear irregular wave forcing on the fatigue life of the foundation and tower of an offshore wind turbine is investigated through aeroelastic calculations. Five representative sea states with increasing significant wave height are considered in a water depth of 40 m. The waves are both linear and fully nonlinear irregular 2D waves. The wind turbine is the NREL 5-MW reference wind turbine. Fatigue analysis is performed in relation to analysis of the sectional forces in the tower and monopile.Impulsive excitation of the sectional force at the bottom of the tower is seen when the waves are large and nonlinear and most notably for small wind speeds. In case of strong velocities and turbulent wind, the excitation is damped out. In the monopile no excitation of the force is seen, but even for turbulent strong wind the wave affects the forces in the pile significantly. The analysis indicates that the nonlinearity of the waves can change the fatigue damage level significantly in particular when the wave and wind direction is misaligned.Copyright

Wave Loads on a Monopile in 3D Waves

During the last decades more and more wind farms have been erected offshore. Most of these wind farms are located at relatively shallow water. The majority of the offshore wind turbines are founded on monopiles. Many of these offshore wind farms are exposed to large and steep waves, in some cases even breaking waves. The loads on the piles caused by waves can be significant and a better knowledge of the forcing caused by real sea states, including irregular waves and directional spreading is required to optimize the design.The present physical model tests have been conducted in order to determine the effects of wave directionality and breaking of irregular waves. Piles with and without secondary structures have been tested. The waves were shoaled over a sloping bed and the pile was placed at two different positions with varying bed slopes. The three forcing components (Fx, Fy, Fz) were measured at the bottom of the pile during the experiments.Breaking waves occurred around the pile in most of the tests and significant slamming forces were observed in the cases where breaking waves hit the pile which is well known from the literature. The experimental results indicated that the slamming force may be reduced when the wave spreading is increased, similar to the case of non-breaking waves.Copyright