An analytical framework is presented to describe the attenuation of regular and irregular waves propagating over floating seaweed farms. Kelp blades suspended on longlines are modelled, as a first approximation, as rigid bars rotating around their upper ends. Assuming small-amplitude blade motions under low to moderate sea conditions, the frequency-dependent transfer function of the rotations can be obtained, with quadratic drag loads linearized. Subsequently, the hydrodynamic problem with regular waves propagating over suspended seaweed canopies is formulated using the continuity equation and linearized momentum equations with additional source terms in the vegetation region. Analytical solutions are obtained for attenuated regular waves with their heights decaying exponentially as they propagate over the canopy. These solutions are utilized as the basis for predicting wave attenuation of irregular waves while stochastic linearization of the quadratic drag loads is employed. In contrast to energy-conservation-based models, which assume the velocity profile follows linear wave theory, the present solution can predict the reduced velocity inside the canopy. The analytical solutions are validated against experimental data and verified against a numerical flow solver. The model is capable of resolving the wave attenuation, along with velocity profiles and phase lag. Drag and inertial force exhibit cancellation effects on wave decay and both affect phase lag.
This paper presents a numerical benchmark study of wave propagation due to a paddle motion using different high-fidelity numerical models, which are capable of replicating the nearly actual physical wave tank testing. A full time series of the measured wave generation paddle motion that was used to generate wave propagation in the physical wave tank will be utilized in each of the models contributed by the participants of International Energy Agency Ocean Energy Systems Task 10, which includes both computational fluid dynamics and smoothed particle hydrodynamics models. The high-fidelity simulations of the physical wave test case will allow for the evaluation of the initial transient effects from wave ramp-up and its evolution in the wave tank over time for two representative regular waves with varying levels of nonlinearity. Metrics like the predicted wave surface elevation at select wave probes, wave period, and phase-shift in time will be assessed to evaluate the relative accuracy of numerical models versus experimental data within specified time intervals. These models will serve as a guide for modelers in the wave energy community and provide a base case to allow further and more detailed numerical modeling of the fixed Kramer Sphere Cases under wave excitation force wave tank testing.
Physical wave basin tests with a focus on uncertainty estimation have been conducted on a fixed sphere subjected to wave loads at Aalborg University as part of the effort of the OES Wave Energy Converters Modeling Verification and Validation (formerly, OES Task 10) working group to increase credibility of numerical modeling of WECs.
The present note defines an idealized test case formulated to accurately represent the physical tests in a simple way. The test case consists of a fixed, rigid sphere half submerged in water subjected to regular waves of three different levels of linearity. The objective of the present note is to allow for numerical tests of the idealized test case.
There are many uncertainties associated with the estimation of extreme loads acting on a wave energy converter (WEC). In this study we perform a sensitivity analysis of extreme loads acting on the Uppsala University (UU) WEC concept. The UU WEC consists of a bottom-mounted linear generator that is connected to a surface buoy with a taut mooring line. The maximum stroke length of the linear generator is enforced by end-stop springs. Initially, a Variation Mode and Effect Analysis (VMEA) was carried out in order to identify the largest input uncertainties. The system was then modeled in the time-domain solver WEC-SIM coupled to the dynamic mooring solver Moody. A sensitivity analysis was made by generating a surrogate model based on polynomial chaos expansions, which rapidly evaluates the maximum loads on the mooring line and the end-stops. The sensitivities are ranked using the Sobol index method. We investigated two sea states using equivalent regular waves (ERW) and irregular wave (IRW) trains. We found that the ERW approach significantly underestimates the maximum loads. Interestingly, the ERW predicted wave height and period as the most important parameters for the maximum mooring tension, whereas the tension in IRW was most sensitive to the drag coefficient of the surface buoy. The end-stop loads were most sensitive to the PTO damping coefficient.
The present paper deals with separation of long-crested regular waves into incident and reflected components. Such methods have been available for several decades for linear waves, but have recently been extended to cover nonlinear waves over horizontal foreshores. The overall goal of the present paper is to extend the separation method for nonlinear regular waves to also cover sloping foreshores. This requires the combination of the existing method with a nonlinear shoaling model. A nonlinear shoaling model was very recently found valid for the shoaling of the primary and bound components in regular waves when the slope angle is positive and mild. In the present paper this shoaling model is utilized and assumed valid also for the de-shoaling of the reflected waves, ie on a negative mild slope angle. However, if the reflected waves are nonlinear the de-shoaling process is much more complicated and will for example cause the release of free waves. Interactions among those free reflected wave components may cause nonlinear interactions not included in the mathematical model. For that reason, the applicability range is limited to mildly nonlinear reflected waves. Using numerical model data with various foreshore slopes, wave nonlinearities and reflection coefficients the reliability of the developed model is examined in detail.