Implementing Nonlinear Buoyancy and Excitation Forces in the WEC-Sim Wave Energy Converter Modeling Tool

Abstract

Wave energy converters (WECs) are commonly designed and analyzed using numerical models that combine multibody dynamics with hydrodynamic models based on the Cummins equation and linearized hydrodynamic coefficients. These modeling methods are attractive design tools because they are computationally inexpensive and do not require the use of highperformance computing resources necessitated by high-fidelity methods, such as Navier-Stokes computational fluid dynamics. Modeling hydrodynamics using linear coefficients assumes that the device undergoes small motions and that the wetted surface area of the devices is approximately constant. WEC devices, however, are typically designed to undergo large motions to maximize power extraction, calling into question the validity of assuming that linear hydrodynamic models accurately capture the relevant fluid-structure interactions.In this paper, we study how calculating buoyancy and Froude-Krylov forces from the instantaneous position of a WEC device changes WEC simulation results compared to simulations that use linear hydrodynamic coefficients. First, we describe the WEC-Sim tool used to perform simulations and how the ability to model instantaneous forces was incorporated into WEC-Sim. We then use a simplified one-body WEC device to validate the model and to demonstrate how accounting for these instantaneously calculated forces affects the accuracy of simulation results, such as device motions, hydrodynamic forces, and power generation.Other aspects of WEC-Sim code development and verification are presented in a companion paper [1] that is also being presented at OMAE2014. INTRODUCTIONWave energy is the most abundant source of marine hydrokinetic energy in the United States and is a plentiful resource around the globe [2]. Recent estimates indicate that the U.S. wave energy resource is 2,600 TWh/year [3]. If it is possible to extract even a small fraction of this energy, there is potential to satisfy a significant amount of U.S. electricity demand [4]. This finding has stimulated commercial and governmental interest in developing wave energy converter (WEC) technologies, and indicates that wave energy could play a significant role in the world's renewable energy portfolio for years to come. Nevertheless, WEC devices are at an early stage of development, corresponding to technology readiness levels (TRLs) 3 through 5, and are not yet a commercially viable technology.Over the past several decades, open-source numerical modeling tools have helped the wind turbine industry achieve commercial viability by enabling the rapid development, analysis, and certification of system designs. The recent emergence of the WEC industry has created a need for a similar set of WEC design and analysis tools that enable the advancement of WEC technologies. Several companies have developed WEC modeling tools, such as WaveDyn, OrcaFlex, and AQWA, that meet many of the needs of the WEC research and development community. Previous experience at the National Renewable Energy Laboratory (NR...

Numerical and Experimental Modelling of a Wave Energy Converter Pitching in Close Proximity to a Fixed Structure

“…The experimental data used for comparison is less reliable for the case of long waves due to reflection effects. Other codes like WEC-Sim, based on the same formulations as the models presented in this paper, have been validated and calibrated [14,16,33] using wave basin experiments as well. However, the published results do not include an experimental validation as complete as that presented in this paper, which makes it difficult to use WEC-Sim for code to code comparison.…”

Nonlinear hydrodynamic and real fluid effects on wave energy converters

“…These latter methodologies focus solely on the Wavestar prototype and rely on empirical fits to laboratory data to include nonlinear terms in the linear model. In contrast, it is hoped the models in development discussed earlier 71,72 can be applied to other WECs.…”

“…The Froude-Krylov force is computed by integrating the time derivative of a linear incident potential (also neglecting the velocity squared pressure term in equation (4)) over the instantaneous wetted surface which in this case is defined as a planar approximation to the intersection line between the incident free surface and the displaced body. A similar approach (with a more accurate evaluation of the nonlinear hydrostatic force) 72 has been adopted to improve the accuracy of the linear open-source WEC simulation software WEC-Sim 73 when applied to devices with highly asymmetric float shapes or devices operating at the upper limit of operating conditions. Gue´rinel et al 70 examine the heave response of a cone with a 1/1.5 radius-to-height ratio in linear regular waves of amplitude 1 m and period 12 s (kA ¼ 0.03) and observe a large (25%) increase in the response amplitude.…”

A Survey of WEC Reliability, Survival and Design Practices

“…The main advantages of working with this type of formulation is the more straightforward ability to include arbitrary nonlinear dynamics as some perturbation from the linear solution. This may include nonlinear hydrodynamics (see, e.g., [73][74][75][76][77]), nonlinear mechanical dynamics, such as due to a mooring system (see, e.g., [78]) or some arbitrary control input (see, e.g., [14,16]). Giorgi and Ringwood [79] performed an assessment of the relative importance of various nonlinear perturbations within a Cummins-style time-domain model and compared computational expenses.…”