Numerical simulation of three-dimensional breaking waves and its interaction with a vertical circular cylinder

The main objective of the paper is to investigate wave impact forces from breaking waves on a monopile substructure for offshore wind turbine in shallow waters. This study examines the load assessment parameters relevant for breaking wave forces on a vertical circular cylinder subjected to breaking waves. Experiments are conducted in a shallow water flume and the wave generation is based on piston type wave maker. The experiments are performed with a vertical circular cylinder with diameter, D = 0.20m which represents a monopile substructure for offshore wind turbines with regular waves of frequencies around 0.8Hz. The experimental setup consists of a 1/10 slope followed by a horizontal bed portion with a water depth of 0.8m. Plunging breaking waves are generated and free surface elevations are measured at different locations along the wave tank from wave paddle to the cylinder in order to find the breaking characteristics. Wave impact pressures are measured on the cylinder at eight different vertical positions along the height of the cylinder under breaking waves for different environmental conditions. The wave impact pressures and wave surface elevations in the vicinity of the cylinder during the impact for three different wave conditions are presented and discussed.

Wave force analysis of the two vertical cylinders by boundary element method

Numerical simulation of wave interaction with vertical circular cylinders of different submergences using immersed boundary method

The diffraction of waves by three bottom fixed vertical circular cylinders is investigated by using the boundary element method. This method has been successfully applied to the isolated vertical circular cylinder and now is used to study the interaction between waves and multiple vertical cylinders. In this paper, a numerical analysis by the boundary element method is developed by the linear potential theory. The numerical analysis by the boundary element method is based on Green's second theorem and introduced to an integral equation for the fluid velocity potential around the vertical circular cylinders. To verify this method, the results obtained in present study are compared with the results computed by the multiple scattering method. The results of the comparisons show strong agreement. Also in this paper, several numerical examples are given to illustrate the effects of various parameters on the wave exciting force such are the separation distance, the wave number and the incident wave angle. This numerical computation method might be used broadly for the design of various offshore structures to be constructed in the future.

ABSTRACTA hybrid-grid 3D non-hydrostatic model is developed and applied to predict nonlinear regular waves interacting with vertical circular cylinders. The model solves unsteady momentum and mass conservation equations by means of an explicit projection method. The 3D grid system is built from a 2D horizontal grid by adding several horizontal layers. The Perot’s scheme is used to treat horizontal advection terms in momentum equations. The 2D horizontal domain is discretized using a hybrid-grid system comprising rectangular and triangular cells to improve the model boundary-flexibility. The numerical model is validated against the experimental data of Stokes wave and cnoidal wave interacting with a vertical circular cylinder, respectively. Good agreement between model results and the experimental data are achieved, demonstrating the capability of the model on resolving interactions between nonlinear regular waves and vertical circular cylinders.

: The magnitude of wave impact loads varies greatly, depending upon whether the wave is breaking, as well as on the wave height, length, steepness, and the geometry and immersion of the impacted structure. This report describes an experiment that was performed to characterize the distribution of breaking and non-breaking wave impact loads over a surface, similar to those performed in 2005 with non-breaking wave impact loads and those performed in 2007 with breaking wave impact loads. In those experiments, the average loads were measured on a flat plate and a cylinder. In order to better understand the distribution of forces over a surface, the impact pressures in this experiment were measured on an instrumented test cube by using an array of slam panels and pressure gages. Plots of impact magnitude trends with wave height, wavelength, draft, and impact angle are presented. Overall, average impact pressures from the breaking waves are greater in magnitude than the impact pressures from the non-breaking waves and average impact pressures tend to increase with increased speed, though there was a dip in pressure at an intermediate speed for some panel locations.

Among different types of loads on jacket structures, wave loads, especially breaking wave loads, are the most likely to threat the stability of the structure; therefore, the correct estimation of the wave loading of an offshore jacket structure is crucial for the design of these structures. Despite the importance of the correct estimation of breaking wave induced forces on jacket structures, so far, no slamming formulae to predict these forces are available in the design standards and guidelines or in other publications. Moreover, the implications of such extreme wave load events and the associated uncertainties for the dynamic response of the entire jacket structure, including the response of the foundation piles, are still not fully clarified. This PhD study attempts to improve the understanding of processes associated with the interaction of waves and jacket structures and to develop reliable wave slamming formulae for the prediction of breaking wave-induced loads on jacket structures. First, the present knowledge is analysed to identify the processes involved in the interaction as well as the related knowledge gaps. Second, the data available from previous tests performed on a truss structure under breaking and non-breaking waves in the Large Wave Flume (GWK tests) in Hannover are analysed to identify the most relevant influencing parameters and to provide reliable slamming formulae for breaking waves on legs and braces of jacket structures. Third, using a CFD model set-up for the waves generated in the large wave flume GWK and a CSD model for the truss structure tested in GWK, the laboratory tests are reproduced and a methodology is proposed to predict total forces induced by near-breaking and breaking waves on jacket structures. Finally, the proposed methodological approach including the slamming force formulae developed in this study is implemented to calculate total forces by breaking waves on a full-scale jacket structure (OC4 jacket). The Finite Element FE model of the OC4 jacket is extended by pile foundation model and the structural performance of the entire structure was examined by comparing the results by those of the numerical models developed for the same jacket structure. Finally, the dynamic response of the jacket structure with pile foundation to breaking waves is systematically analysed to achieve a substantially improved understanding of the processes involved in the wave-jacket-pile foundation interaction.

A pressure impulse model is presented for wave impact on vertical circular cylinders. Pressure impulse is the time integral of the pressure during an impact of short time scale. The model is derived for a simplistic geometry and has relative impact height, crest length and cylinder radius as effective variables. The last parameter, the maximum angle of impact, is free and can be calibrated to yield the right force impulse. A progression of simpler pressure impulse models are derived in terms of a three-dimensional box generalization of the two-dimensional wall model and an axisymmetric model for vertical cylinders. The dependence on the model parameters is investigated in the simpler models and linked to the behaviour of the three-dimensional cylinder model. The model is next validated against numerical results for a wave impact for a phase- and direction-focused wave group. The maximum impact angle is determined by calibration against the force impulse. A good match of the pressure impulse fields is found. Further comparison to the force impulse of two common models in marine engineering reveals improved consistency for the present model. The model is found to provide a promising representation of the pressure impulse field, based on a limited number of input parameters. Its further validation and potential as a robust tool in force and response prediction is discussed.

An accurate description of extreme waves is necessary in order to estimate maximum wave forces on offshore structures. On several occasions freak waves have been observed in the past, some causing severe damage. In order to model such extreme wave conditions with a computational fluid dynamics (CFD) model, emphasize needs to be put on the wave generation. One possibility is to use focused waves of first or second order based on irregular sea state wave spectra. For focused waves, the wave phase is chosen, so that the waves focus in a predetermined location at a specified time. Numerical tests have shown, that generating extreme waves based on this method is somewhat limited. The individual wave components are steep enough, that they start to break before the focus location. In the current paper, transient wave packets are used for extreme wave generation. This way, extreme waves can be generated that are higher, but only break at the concentration point. The transient wave packets method is implemented in the open-source CFD software REEF3D. This model uses the level set method for interface capturing. For the hydrodynamics, the Navier-Stokes equations are solved in three dimensions. The code employs a staggered Cartesian mesh, ensuring tight pressure-velocity coupling. Complex geometries are handled with a ghost cell immersed boundary method. High-performance computing is enabled through domain decomposition based parallelization. Convection discretization of the different flow variables is performed with the fifth-order WENO (weighted essentially non-oscillatory) scheme. For the explicit time treatment a third-order Runge-Kutta scheme is selected. In order to validate the extreme wave generation, numerical tests in an empty wave tank are performed and compared with experimental data. Then, the extreme wave breaking on a vertical circular cylinder is investigated.

Large-scale random-wave experiments (H a = 1.3 m, f p = 0.17 Hz, d = 5.0 m) on a vertical circular cylinder (D = 0.5 m), having a roughness of about 60 µm, were performed to study the wave loading in the free surface zone at high Reynolds numbers (up to 7·105). Some first results of the data analysis are presented, showing characteristic time histories of velocities, pressures, and in-line forces. Also the energy density spectra and exceedance curves for both the maximum and the minimum inline-force are compared at two levels, z = 0 m and z = −2.3 m..

Wave-current interaction, a common phenomenon in the areas of estuary and gulf, is also notable in deep water sea area. When the current is strong enough, wave “blocking” accompanied by wave breaking takes place and leads to hazard sea conditions. On the other hand, wave countering current is also thought to be one of the main causes of occurrence of rogue waves in the ocean, which imperils offshore structures and is of much importance for research. Knowing this, viscous flow of wave generation on current is simulated by using Reynolds-Averaged-Navier-Stokes (RANS) equation for better understanding of its mechanism and flow field. In this study, two-dimensional waves propagating without current, along and against pre-existing large-scale current have been investigated. The validation of calculation has been demonstrated through comparing with preliminary experiments in Circulating Water Channel (CWC). When propagating in counter-current, wave is steepened and wave height increases dramatically, thus wave breaking occurs occasionally. Therefore, the variation of wave height and steepness with current velocity has been analyzed quantitatively. It has been confirmed that wave “blocking” occurs when current speed is comparable with group velocity of waves. And this is analyzed in detail in terms of kinematics, energy transfer and others. Accordingly, wave breaking is evaluated by the well-known classical wave breaking criterion. Furthermore, the proposed viscous model is compared with “simple bore dissipation model” to evaluate energy dissipation of wave breaking and improvement of numerical model for wave blocking is introduced. It has been shown that the present numerical model is applicable to reproduce the wave blocking and breaking phenomenon and it will be useful for future engineering purpose on predicting real sea conditions.

When bottom mounted structures of large displacement are immersed in the sea, earthquake induced hydrodynamic loads may become important design factors. Specifically, as the earth oscillates, a bottom mounted structure is forced to describe time dependent motion in an otherwise still fluid. As a result, hydrodynamic loads in addition to the inertial loads of the structure itself are induced. In this paper, a theoretical approach to the calculation of these hydrodynamic loads is outlined and numerical results are presented for several submerged configurations. Practical geometries considered include a submerged oil storage tank configuration and a conical configuration as has been proposed for offshore drilling rig designs for deployment in the Arctic. Also, computations were carried out for a sphere and vertical circular cylinder and various comparisons with classical results are made. Numerical results for these submerged structures are presented in the form of a dimensionless hydrodynamic load parameter or added mass coefficient. Results corresponding to a number of different water depths are presented to show the rather sizable effect of the relative water depth on the hydrodynamic force. It is shown that for typical earthquake frequencies, the effect of the free water surface is to reduce the hydrodynamic loads in comparison to the corresponding infinite depth values. Experimental results obtained by vibration testing are presented for a submerged sphere and a vertical circular cylinder. These results show excellent agreement with the theoretical results. Introduction Principal attention in earthquake engineering has been given to the generation of tsunami waves, the shoreline run-up and damage caused by these waves, as well as the damage to dry land structures caused by strong ground motion. With the increased deployment of large submerged structures, an additional facet of this important problem has come to light. Namely, if a large bottom mounted structure submerged in the ocean is excited by oscillatory ground motion, hydrodynamic loads in addition to its own inertia forces come into play. As the structure is caused to move through the water, hydrodynamic forces which are dependent upon the size and shape of the structure as well as the water depth and frequency of oscillation arise. On account of the large density of water, these forces are often quite large and have considerable influence on the structural design. When an object is accelerated through a fluid there are, in general, two types of forces that are recognized, one being a drag component and a second, the inertial component. The nature of the flow produced by the time dependent motion of the immersed rigid object and the relative contribution of these two components of force is generally considered to be strongly dependent on the amplitude of the relative fluid motion in comparison to the characteristic lineal dimension of the object. For example, Keulegan and Carpenter [1] found that, for harmonic motion of the fluid past a fixed circular cylinder, major flow separation did not occur and the forces were well represented by potential flow values provided the amplitude of the motion was less than about a half diameter.

Finite volume scheme for the solution of 2D extended Boussinesq equations in the surf zone

Use of mesh adaptivity in simulation of flow in packed beds – A case study

Prediction of breaking wave forces on vertical cylinders