Relevance of pressure field accuracy for nonlinear Froude–Krylov force calculations for wave energy devices

Abstract

Due to their computational convenience, linear mathematical models for wave energy converters are usually employed. Including nonlinearities may improve the accuracy of the results, but often at the price of an additional computational and complexity burden, which can be justified only if nonlinearities are significant. One of the sources of nonlinearity in fluid-body interactions is the wave field itself. Different wave models exist, among which are linear Airy's theory, Wheeler's stretching approach, the nonlinear Rienecker-Fenton method, and higher order spectral methods, all of which achieve a different compromise of accuracy and complexity. The impact of the accuracy of such wave theories strongly depends on the specific device (operating principle, power production region or survivability mode), and installation site (water depth, occurrences of each sea state in the scatter diagram of the installation site). This paper evaluates the performance of different wave field representations, firstly in absolute terms and, secondly, in relation to the associated computation of nonlinear Froude-Krylov forces for different wave energy devices, in regular and irregular sea states. It is shown that Wheeler's stretching offers a good accuracy/complexity compromise for WECs operating in the power production region.

A Blind Comparative Study of Focused Wave Interactions with Floating Structures (CCP-WSI Blind Test Series 3)

“…This numerical method implements nonlinear kinematics and nonlinear Froude-Krylov force calculations in a linear potential theory-based framework (Giorgi & Ringwood, 2018a). The waves are a linear superposition of components, derived from the surface elevation at probe 5 in the empty tank tests, propagated using linear dispersion and including Wheeler-stretching (Giorgi & Ringwood, 2018b). A fixed time-step of 0.04 s is used.…”

Assessment of Scale Effects, Viscous Forces and Induced Drag on a Point-Absorbing Wave Energy Converter by CFD Simulations

“…They also highlight the difference in flow pattern surrounding the WEC for the different body shapes and put forward viscous correction factors, which are deduced from the deviation of the WEC decay motion from potential theory. In a recent series of papers Giorgi and co-authors [14,21,22] discuss a case study of a spherical floater in heave. They show that weakly non-linear potential flow simulations with calibrated parametrised drag force give results much closer to CFD prediction than simulations using only nonlinear FK corrections.…”

A Compact 6-DoF Nonlinear Wave Energy Device Model for Power Assessment and Control Investigations

“…where p st = −γz is the static pressure, p dy the dynamic pressure, γ the specific weight of the sea water, η(x, t) a 2dimensional wave with amplitude a and wave frequency ω, χ the wave number, h the water depth (defined according to a right-handed inertial frame of reference (x, y, z), with the origin at the still water level (SWL)), x pointing in the direction of propagation of the wave, and z pointing upwards. It is then convenient to apply Wheeler's stretching to (1), as shown in [12]. Note that, in irregular sea conditions, the pressure formulation in (1) is used for each harmonic component of the wave spectrum in order to define the total pressure field.…”

“…Note that, in irregular sea conditions, the pressure formulation in (1) is used for each harmonic component of the wave spectrum in order to define the total pressure field. The accuracy of the pressure representation, and the effectiveness of the nonlinear FK force calculation is discussed in [12], for regular and irregular sea states, also considering nonlinear wave models, such as Rienecker-Fenton, for regular waves, and higher-order spectral (HOS) method for irregular waves, concluding that the use of Wheeler's stretching allows for sufficiently accurate computation of nonlinear FK force, even with nonlinear waves.…”