Since time-domain simulations of wave energy converters are computationally expensive, how can we analyse their dynamics and test wide ranges of design variables, without simplifying the physics involved? One possible solution is the use of General Polynomial Chaos (gPC). GPC provides computationally efficient surrogate models for partial differential equation based models, which are particularly useful for sensitivity analysis and uncertainty quantification. We demonstrate the application of gPC to study the dynamics of a wave energy converter in an operational sea-state, when there is uncertainty in the values of the stiffness and damping coefficient of the power take-off.
A 3D fully nonlinear potential flow (FNPF) model based on an Eulerian formulation is presented. The model is discretized using high-order prismatic – possibly curvi-linear – elements using a spectral element method (SEM) that has support for adaptive unstructured meshes. The paper presents details of the FNPF-SEM development and the model is illustrated to exhibit exponential convergence. The model is then applied to the case of focused waves impacting on a surface-piecing fixed FPSO-like structure. Good agreement was found between numerical and experimental wave elevations and pressures.
The International Energy Agency Technology Collaboration Program for Ocean Energy Systems (OES) initiated the OES Wave Energy Conversion Modeling 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 modeling 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.
The paper discusses the use of CFD simulations to analyse the parametric excitation of moored, full scale wave energy converters in six degrees of freedom. We present results of VOF-RANS and VOF-Euler simulations in OpenFOAM!R for two body shapes: (i) a truncated cylinder; and (ii) a cylinder with a smooth hemispherical bottom. Flow characteristics show large differences in smoothness of flow between the hull shapes, where the smoother shape results in a larger heave response. However the increased amplitude makes it unstable and parametric pitch excitation occurs with amplitudes up to 30". The responses in surge, heave and pitch (including the transition to parametric motion) are found to be insensitive to the viscous effects. This is notable as the converters are working in resonance. The effect of viscous damping was visible in the roll motion, where the RANS simulations showed a smaller roll. However, the roll motion was found to be triggered not by wave-body interaction with the incident wave, but by reflections from the side walls. This highlights the importance of controlling the reflections in numerical wave tanks for simulations with WEC motion in six degrees of freedom.
This paper analyzes the nonlinear forces on a moored point-absorbing wave energy converter (WEC) in resonance at prototype scale (1:1) and at model scale (1:16). Three simulation types were used: Reynolds Averaged Navier-Stokes (RANS), Euler and the linear radiation-diffraction method (linear). Results show that when the wave steepness is doubled, the response reduction is: (i) 3% due to the nonlinear mooring response and the Froude-Krylov force; (ii) 1-4% due to viscous forces; and (iii) 18-19% due to induced drag and non-linear added mass and radiation forces. The effect of the induced drag is shown to be largely scale-independent. It is caused by local pressure variations due to vortex generation below the body, which reduces the total pressure force on the hole. Euler simulations are shown to be scale-independent and the scale effects of the WEC are limited by the purely viscous contribution (1-4%) for the two waves studied. We recommend that experimental model scale test campaigns of WECs should be accompanied by RANS simulations, and the analysis complemented by scale-independent Euler simulations to quantify the scale-dependent part of the nonlinear effects.
A coupling between a dynamic mooring solver based on high-order finite element techniques (MooDy) and a radiation-diffraction based hydrodynamic solver (WEC-Sim) is presented. The high-order scheme gives fast convergence resulting in high-resolution simulations at a lower computational cost. The model is compared against a lumped mass mooring code (MoorDyn) that has an existing coupling to WEC-Sim. The two models are compared for a standard test case and the results are similar, giving confidence in the new WEC-Sim-MooDy coupling. Finally, the coupled model is validated using experimental data of a spread moored cylinder with good agreement.
The wave loads and the resulting motions of floating wave energy converters are traditionally computed using linear radiation–diffraction methods. Yet for certain cases such as survival conditions, phase control and wave energy converters operating in the resonance region, more complete mathematical models such as computational fluid dynamics are preferred and over the last 5 years, computational fluid dynamics has become more frequently used in the wave energy field. However, rigorous estimation of numerical errors, convergence rates and uncertainties associated with computational fluid dynamics simulations have largely been overlooked in the wave energy sector. In this article, we apply formal verification and validation techniques to computational fluid dynamics simulations of a passively controlled point absorber.
The phase control causes the motion response to be highly nonlinear even for almost linear incident waves. First, we show that the computational fluid dynamics simulations have acceptable agreement to experimental data. We then present a verification and validation study focusing on the solution verification covering spatial and temporal discretization, iterative and domain modelling errors. It is shown that the dominating source of errors is, as expected, the spatial discretization, but temporal and iterative errors cannot be neglected. Using hexahedral cells with low aspect ratio and 30 cells per wave height, we obtain results with less than 5% uncertainty in motion response (except for surge) and restraining forces for the buoy without phase control. The amplified nonlinear response due to phase control caused a large increase in numerical uncertainty, illustrating the difficulty to obtain reliable solutions for highly nonlinear responses, and that much denser meshes are required for such cases.
This paper contributes to the understanding of competition and industry evolution by analyzing how submarket dynamics and agency influence the development of the emerging industrial field of Danish offshore wind energy. We argue that industry evolution is sensitive to the balance between integration, overlap and disintegration across submarkets. This balance depends on how strategic intent and behavior influence submarket dynamics, leading to the conclusion that effects of agency and managerial intent should play a more prominent role in studies of industry evolution.
Computational fluid dynamics (CFD) is becoming an increasingly popular tool in the wave energy sector, and over the last five years we have seen many studies using CFD. While the focus of the CFD studies have been on the validation phase, comparing numerically obtained results against experimental tests, the uncertainties associated with the numerical solution has so far been more or less overlooked. There is a need to increase the reliability of the numerical solutions in order to perform simulation based optimization at early stages of development. In this paper we introduce a well-established verification and validation (V&V) technique. We focus on the solution verification stage and how to estimate spatial discretization errors for simulations where no exact solutions are available. The technique is applied to the cases of a 2D heaving box and a 3D moored cylinder. The uncertainties are typically acceptable with a few percent for the 2D box, while the 3D cylinder case show double digit uncertainties. The uncertainties are discussed with regard to physical features of the flow and numerical techniques.
The present paper describes the work carried out in the project ’Mooring Solutions for Large Wave Energy Converters’, which is a Danish research project carried out in a period of three years from September 2014, with the aim of reducing cost of the moorings for four wave energy converters and improving the applied design procedure. The paper presents the initial layouts and costs and illustrates which solutions could potentially reduce cost. Different methods for analysis of the systems were applied, ranging from simple quasi-static analysis to full dynamic analysis and experimental work. The numerical methods were compared to the experimental data, and results showed significant underestimation of tensions in the quasi-static model while reasonable overestimation was found in the dynamic analysis even without major tuning of the model. The dynamic analysis has then been implemented in a meta-model based optimization process with the aim of optimizing the mooring layout for each WEC according to cost of the systems.