Cambridge Core - Thermal-Fluids Engineering - Ocean Waves and Oscillating Systems - by Johannes Falnes

A floating air bag, ballasted in water, expands and contracts as it heaves under wave action. Connecting the bag to a secondary volume via a turbine transforms the bag into a device capable of generating useful energy from the waves. Small-scale measurements of the device reveal some interesting properties, which are successfully predicted numerically. Owing to its compressibility, the device can have a heave resonance period longer than that of a rigid device of the same shape and size, without any phase control. Furthermore, varying the amount of air in the bag is found to change its shape and hence its dynamic response, while varying the turbine damping or the air volume ratio changes the dynamic response without changing the shape.

This paper deals with the optimization of wave absorbers oscillating about a fixed submerged horizontal axis. A multiobjective optimization algorithm is employed to search for the optimal geometries where two cost criteria are used as the objective functions to be minimized. The two cost criteria are the ratios, integrated over a specified frequency range, of the submerged surface area to the maximum absorbed power, and of the maximum reaction force to the maximum absorbed power. Geometric configurations with uniform simple cross-sectional shapes, viz. line, circle, and elliptical sections, are considered. For each configuration, the body dimensions and submergence, as well as the submergence of the rotation axis, are the variables to be optimized. It is found that most of the optimal geometries have their rotation axes close to the sea bottom and their bodies close to the free surface. The optimal size of the geometries varies depending on the selected wave frequency range, but the optimal cross-sectional dimensions are generally less than one third of the water depth when optimized over a uniform distribution of wave frequencies from 0.4 to 1.3 rad/s. Among the cross sections considered, the elliptical one performs best.

The time-average wave power that is absorbed from an incident wave by means of a wave-energy conversion (WEC) unit, or by an array of WEC units—i.e. oscillating immersed bodies and/or oscillating water columns (OWCs)—may be mathematically expressed in terms of the WEC units' complex oscillation amplitudes, or in terms of the generated outgoing (diffracted plus radiated) waves, or alternatively, in terms of the radiated waves alone. Following recent controversy, the corresponding three optional expressions are derived, compared and discussed in this paper. They all provide the correct time-average absorbed power. However, only the first-mentioned expression is applicable to quantify the instantaneous absorbed wave power and the associated reactive power. In this connection, new formulae are derived that relate the ‘added-mass’ matrix, as well as a couple of additional reactive radiation-parameter matrices, to the difference between kinetic energy and potential energy in the water surrounding the immersed oscillating WEC array. Further, a complex collective oscillation amplitude is introduced, which makes it possible to derive, by a very simple algebraic method, various simple expressions for the maximum time-average wave power that may be absorbed by the WEC array. The real-valued time-average absorbed power is illustrated as an axisymmetric paraboloid defined on the complex collective-amplitude plane. This is a simple illustration of the so-called ‘fundamental theorem for wave power’. Finally, the paper also presents a new derivation that extends a recently published result on the direction-average maximum absorbed wave power to cases where the WEC array's radiation damping matrix may be singular and where the WEC array may contain OWCs in addition to oscillating bodies.

The International Energy Agency Technology Collaboration Programme for Ocean Energy Systems (OES) initiated the OES Wave Energy Conversion Modelling Task, which focused on the verification and validation of numerical models for simulating wave energy converters (WECs). The long-term goal is to assess the accuracy of and establish confidence in the use of numerical models used in design as well as power performance assessment of WECs. To establish this confidence, the authors used different existing computational modelling tools to simulate given tasks to identify uncertainties related to simulation methodologies: (i) linear potential flow methods; (ii) weakly nonlinear Froude–Krylov methods; and (iii) fully nonlinear methods (fully nonlinear potential flow and Navier–Stokes models). This article summarizes the code-to-code task and code-to-experiment task that have been performed so far in this project, with a focus on investigating the impact of different levels of nonlinearities in the numerical models. Two different WECs were studied and simulated. The first was a heaving semi-submerged sphere, where free-decay tests and both regular and irregular wave cases were investigated in a code-to-code comparison. The second case was a heaving float corresponding to a physical model tested in a wave tank. We considered radiation, diffraction, and regular wave cases and compared quantities, such as the WEC motion, power output and hydrodynamic loading.