Cylindrical linear water waves and their application to the wave-body problem

The interaction between water waves and a floating or fixed body is bi-directional: wave forces act on and cause motion in the body, and the body alters the wave field. The impact of the body on its wave field is important to understand because: 1) it may have positive or negative consequences on the natural or built environment; 2) multiple bodies in proximity interact via the waves that are scattered and radiated by them; and 3) in ocean wave energy conversion, by conservation of energy, as a device absorbs energy, so too must the energy be removed from the wave field. Herein, the cylindrical solutions to the linear wave boundary-value problem are used to analyze the floating body wave field. These solutions describe small-amplitude, harmonic, potential-flow waves in the form of a Fourier summation of incoming and outgoing, partial, cylindrical, wave components. For a given geometry and mode of motion, the scattered or radiated waves are characterized by a particular set of complex cylindrical coefficients. A novel method is developed for finding the cylindrical coefficients of a scattered or radiated wave field by making measurements, either computationally or experimentally, over a circular-cylindrical surface that circumscribes the body and taking a Fourier transform as a function of spatial direction. To isolate evanescent modes, measurements are made on the free-surface and as a function of depth. The technique is demonstrated computationally with the boundary-element method software, WAMIT. The resulting analytical wave fields are compared with those computed directly by WAMIT and the match is found to be within 0.1%. A similar measurement and comparisons are made with experimental results. Because of the difficulty in making depth-dependent measurements, only free-surface measurements were made with a circular wave gauge array, where the gauges were positioned far from the body in order to neglect evanescent modes. The experimental results are also very good. However, both high-order harmonics and wave reflections led to difficulties. To compute efficiently the wave interactions between multiple bodies, a well-known multiple-scattering theory is employed, in which waves that are scattered and radiated by one body are considered incident to another body, which in turn radiates and scatters waves, sending energy back to the first. Wave fields are given by their cylindrical representations and unknown scattered wave amplitudes are formulated into a linear system to solve the problem. Critical to the approach is the characterization of, for each unique geometry, the cylindrical forces, the radiated wave coefficients, and the scattered waves in the form of the diffraction transfer matrix. The method developed herein for determining cylindrical coefficients is extended to new methods for finding the quantities necessary to solve the interaction problem. The approach is demonstrated computationally with WAMIT for a simple cylinder and a more complex wave energy converter (WEC). Multiple-scattering computations are verified against direct computations from WAMIT and are performed for spectral seas and a very large array of 101 WECs. The multiple-scattering computation is 1,000- 10,000 times faster than a direct computation because each body is represented by 10s of wave coefficients, rather than 100s to 1,000s of panels. A new expression for wave energy absorption using cylindrical coefficients is derived, leading to a formulation of wave energy absorption efficiency, which is extended to a nondimensional parameter that relates to efficiency, capture width and gain. Cylindrical wave energy absorption analysis allows classical results of heaving and surging point absorbers to be easily reproduced and enables interesting computations of a WEC in three-dimensions. A Bristol Cylinder type WEC is examined and it is found that its performance can be improved by flaring its ends to reduce "end effects". Finally, a computation of 100% wave absorption is demonstrated using a generalized incident wave. Cylindrical representations of linear water waves are shown to be effective for the computations of wave-body wave fields, multi-body interactions, and wave power absorption, and novel methods are presented for determining cylindrical quantities. One of the approach's greatest attributes is that once the cylindrical coefficients are found, complex representations of waves in three dimensions are stored in vectors and matrices and are manipulated with linear algebra. Further research in cylindrical water waves will likely yield useful applications such as: efficient computations of bodies interacting with short-crested seas, and continued progress in the understanding of wave energy absorption efficiency

Overview of open source codes to assess environmental effects of ocean wave farms (Extended Abstract)

The United States has a theoretical ocean wave energy resource potential of 1,594–2,640 TWh/year, enough to power between 143.5 and 237.6 million homes/year and contribute substantially to the United States’ energy portfolio [1]. However, wave energy converters (WECs) are currently in the early stages of research and development at low technology readiness levels. Open ocean deployment data is from demonstration-scale projects, not from utility-scale deployments. As a result, researchers, developers, and regulators rely heavily on numerical models to understand the environmental effects of wave farms. Preliminary numerical studies have demonstrated that small-scale deployments of ~10 WECs or less have little to no impact on the physical environment. But utility-scale wave farms may affect the near-field and nearshore wave environment, circulation patterns, and nearshore processes such as sediment transport. A suite of open source codes has been developed by Sandia National Laboratories focused on simulating the energy extraction of WECs to better understand and predict their potential environment effects

Overview of open source codes to assess environmental effects of ocean wave farms (Extended Abstract)

The United States has a theoretical ocean wave energy resource potential of 1,594–2,640 TWh/year, enough to power between 143.5 and 237.6 million homes/year and contribute substantially to the United States’ energy portfolio [1]. However, wave energy converters (WECs) are currently in the early stages of research and development at low technology readiness levels. Open ocean deployment data is from demonstration-scale projects, not from utility-scale deployments. As a result, researchers, developers, and regulators rely heavily on numerical models to understand the environmental effects of wave farms. Preliminary numerical studies have demonstrated that small-scale deployments of ~10 WECs or less have little to no impact on the physical environment. But utility-scale wave farms may affect the near-field and nearshore wave environment, circulation patterns, and nearshore processes such as sediment transport. A suite of open source codes has been developed by Sandia National Laboratories focused on simulating the energy extraction of WECs to better understand and predict their potential environment effects

Computation of the Diffraction Transfer Matrix and the Radiation Characteristics in the open source zero-order BEM code NEMOH

International audienceThis paper presents a comparison of the hydrodynamic operators DTM and RC of a cylinder computed with the BEM solver NEMOH, in which the methodology of [2] has been implemented, and the ones obtained with the alternative approach developed and validated by [7]. In addition, a comparison of the wavefield of a small array of 4 freely floating cylinders computed using both the interaction theory and with a direct NEMOH calculation is shown

Overview of Open Source Codes to Assess Environmental Effects on Ocean Wave Farms

The development of SNL-SWAN by Sandia National Laboratories (SNL) allows users to investigate the interaction between a WEC or WEC array and the wave environment. SNL-SWAN when coupled with a hydrodynamic and sediment transport model such as Delft3D, developed by Deltares Inc, allows for the direct investigation of WEC array effects on the physical environment (e.g. waves, currents, seabed) and the associated site ecology. Ongoing development of these tools has shown how the coupling of SNL-SWAN with Delft3D-Flow can quantify the interaction between device(s) and the hydrodynamic environment at a real-world site

Wave Energy Converter Modeling in the Frequency Domain : A Design Guide

Wave energy converter research continues to advance and new developers are continuing to emerge, leading to the need for a general modeling methodology. This work attempts to outline the design methodology necessary to perform frequency domain analysis on a generic wave energy converter. A two-body point absorber representing a generic popular design was chosen and a general procedure is presented showing the process to obtain first pass preliminary performance results. The result is a design guide that new developers can adapt to their particular design and wave conditions, which will provide the first steps toward a cost of energy estimate. This will serve the industry by providing a sound methodology to accelerate the new development of wave energy converters

Waves, WEC, and Arrays

This presentation was given as part of Oregon State University's College of Oceanographic and Atmospheric Sciences graduate student seminar series. It is critical to understand waves dynamics in order to design wave energy convertors and then deploy them in arrays. Modelling suggests that array interactions lead to constructive and destructive interference

Cylindrical Wave Field Experiments - Raw Data

<p>This fileset contains the raw data files from the experiments. Matlab scripts for processing the data can be found at:</p> <p> https://github.com/camalamadingdong/cyl_wfe</p> <p>Experiments were conducted in the University of Edinburgh Curved Wave Tank to determine the linear cylindrical coefficients for progressive water waves. The experiments employed two body geometries, an attenuator consisting of a horizontal pitching cylinder, and a terminator made up of a bottom-hinged flap. An array of 59 wave gauges was arranged in a circle-spoke pattern, where the circle of wave gauges was necessary for deriving the cylindrical coefficients, and the spokes, which extended radially further afield, were used for validation. Both the scattered and the radiated waves of the bodies were examined at three frequencies.</p> <p> </p