This project has received funding from the European Union’s Horizon 2020
research and innovation programme
Parametric excitation in the pitch/roll degrees of freedom (DoFs) can induce dynamic instability in floating cylinder-type structures such as spar buoys, floating offshore wind or wave energy converters. At certain frequency and amplitude ranges of the input waves, parametric coupling between the heave and pitch/roll DoFs results in undesirable large amplitude rotational motion. One possible remedy to mitigate the existence of parametric resonance is the use of dynamic vibration absorbers. Two prominent types of dynamic vibration absorbers are tuned mass dampers (TMDs) and nonlinear energy sinks (NESs), which have contrasting properties with regard to their amplitude and frequency dependencies when absorbing kinetic energy from oscillating bodies. This paper investigates the suppression of parametric resonance in floating bodies utilizing dynamic vibration absorbers, comparing the performance of TMDs against NESs for a test case considering a floating vertical cylinder. In addition to the type of dynamic vibration absorber utilized, the paper also examines the DoF which it acts on, comparing the benefits between attaching the vibration Read
The oscillating-water-column (OWC) spar-buoy is a type of wave energy converter that may exhibit undesirable large roll and pitch amplitudes caused by a dynamic instability induced by parametric resonance. The occurrence of this phenomenon not only reduces the power extraction but significantly increases the structural loads on the buoy, the turbine rotor and on the mooring system. The paper compares the parametric resonance behaviour of two configurations of an OWC spar-buoy using experimental data obtained in a wave flume at a scale of 1:100. The configurations investigated were: (1) closed and (2) fully open-air chamber. The experimental tests covered a wide range of regular and irregular waves, as well as in free decay experiments. Results showed that opening the air chamber reduces the coupling between the buoy and the OWC within, thus shifting the damped natural heave frequency of the system in comparison with the closed chamber configuration. This effect changes parametric resonance characteristics of the two configurations due to the coupling between roll/pitch and heave modes. Moreover, for specific wave frequencies, the occurrence of parametric resonance observed when the chamber is closed do not occur while the air chamber is fully open. These results suggest the possibility of controlling a pressure relief valve installed on top of the device to reduce parametric resonance whenever this dynamic instability is detected. Read
This review focuses on the most suitable form of hydrodynamic modeling for the next generation wave energy converter (WEC) design tools. To design and optimize a WEC, it is estimated that several million hours of operation must be simulated, perhaps one million hours of WEC simulation per year of the R&D program. This level of coverage is possible with linear potential flow (LPF) models, but the fidelity of the physics included is not adequate. Conversely, while Reynolds averaged Navier–Stokes (RANS) type computational fluid dynamics (CFD) solvers provide a high fidelity representation of the physics, the increased computational burden of these models renders the required amount of simulations infeasible. To scope the fast, high fidelity options, the present literature review aims to focus on what CFD theories exist intermediate to LPF and RANS as well as other modeling options that are computationally fast while retaining higher fidelity than LPF. Read
Parametric resonance is a dynamic instability due to the internal transfer of energy between degrees of freedom. Parametric resonance is known to cause large unstable pitch and/or roll motions in floating bodies, and has been observed in wave energy converters (WECs). The occurrence of parametric resonance can be highly detrimental to the performance of a WEC, since the energy in the primary mode of motion is parasitically transferred into other modes, reducing the available energy for conversion. In addition, the large unstable oscillations produce increased loading on the WEC structure and mooring system, accelerating fatigue and damage to the system. To remedy the negative effects of parametric resonance on WECs, control systems can be designed to mitigate the onset of parametric resonance. A key element of such a control system is a real-time detection system, which can provide an early warning of the likely occurrence of parametric resonance, enabling the control system sufficient time to respond and take action to avert the impending exponential increase in oscillation amplitude. This paper presents the first application of a real-time detection system for the onset of parametric resonance in WECs. The method is based on periodically assessing the stability of a mathematical model for the WEC dynamics, whose parameters are adapted online, via a recursive least squares algorithm, based on online measurements of the WEC motion. The performance of the detection system is demonstrated through a case study, considering a generic cylinder type spar-buoy, a representative of a heaving point absorber WEC, in both monochromatic and polychromatic sea states. The detection system achieved 95% accuracy across nearly 7000 sea states, producing 0.4% false negatives and 4.6% false positives. For the monochromatic waves more than 99% of the detections occurred while the pitch amplitude was less than 1/6 of its maximum amplitude, whereas for the polychromatic waves 63% of the detections occurred while the pitch amplitude was less than 1/6 of its maximum amplitude and 91% while it was less than 1/3 of its maximum amplitude. Read
Mathematical models are essential for the design and control of offshore systems, to simulate the fluid–structure interactions and predict the motions and the structural loads. In the development and derivation of the models, simplifying assumptions are normally required, usually implying linear kinematics and hydrodynamics. However, while the assumption of linear, small amplitude motion fits traditional offshore problems, in normal operational conditions (it is desirable to stabilize ships, boats, and offshore platforms), large motion and potential dynamic instability may arise (e.g., harsh sea conditions). Furthermore, such nonlinearities are particularly evident in wave energy converters, as large motions are expected (and desired) to enhance power extraction. The inadequacy of linear models has led to an increasing number of publications and codes implementing nonlinear hydrodynamics. However, nonlinear kinematics has received very little attention, as few models yet consider six degrees of freedom and large rotations. This paper implements a nonlinear hydrodynamic and kinematic model for an archetypal floating structure, commonplace in offshore applications: an axisymmetric spar-buoy. The influence of nonlinear dynamics and kinematics causing coupling between modes of motion are demonstrated. The nonlinear dynamics are shown to cause parametric resonance in the roll and pitch degrees of freedom, while the nonlinear kinematics are shown to potentially cause numerical instability in the yaw degree of freedom. A case study example is presented to highlight the nonlinear dynamic and kinematic effects, and the importance of including a nominal restoring term in the yaw DoF presented. Read
An active control method, to suppress the onset of pitch/roll parametric resonance on an oscillating water column (OWC) spar buoy, is proposed in this paper, which utilises a pressure relief valve at the top of the OWC air chamber. The paper examines the hypothesis that by opening the relief valve, to reduce the air chamber pressure difference and to decouple the dynamics of the spar buoy and the OWC within, the natural pitch/roll frequen- cies of the system will be shifted, allowing parametric resonance to be cancelled when its onset is detected. The paper reports on experiments, performed to test the stated hypothesis, with a small-scale model OWC spar buoy in a wave flume. Two config- urations are considered and tested in a range of monochromatic waves (1) fully closed air chamber; (2) fully open chamber. The results partially confirm the hypothesis, demonstrating that the occurrence of parametric resonance observed for certain wave frequencies when the chamber is closed does not occur when the chamber is open. However, the change in the natural pitch/roll frequencies between the two configurations is very small, and parametric resonance occurs in both confurations for waves with twice this frequency. Read
Exploiting parametric resonance may enable increased performance for wave energy converters (WECs). By designing the geometry of a heaving WEC, it is possible to introduce a heave-to-heave Mathieu instability that can trigger parametric resonance. To evaluate the potential of such a WEC, a mathematical model is introduced in this paper for a heaving buoy with a non- constant waterplane area in monochromatic waves. The efficacy of the model in capturing parametric resonance is verified by a comparison against the results from a nonlinear Froude–Krylov force model, which numerically calculates the forces on the buoy based on the evolving wetted surface area. The introduced model is more than 1000 times faster than the nonlinear Froude–Krylov force model and also provides the significant benefit of enabling analytical investigation techniques to be utilised. Read
Numerical wave tanks (NWTs) are an essential tool for wave energy converter (WEC) development. Due to it's opensource nature and wide user base, OpenFOAM is proving to be an eective software platform for implementing NWTs for WEC experiments. Indeed, in a recent review of Computational Fluid Dynamics based NWTs (CNWTs) for WECs, OpenFOAM was the most prominately used CFD software (39% of total). Dynamic mesh motion can prove a challenge during WEC simulation, due to factors such as: (a) large ampitude body motions when a WEC is driven into resonance, with the input waves, by an energy maximising control system (EMCS) [9], (b) multiple degree of freedom (DoF) motion by a oating WEC, and/or (c) multi-body WEC with dierent sections oscillating in close proximity to each other. Fortunately, the overset method has recently become available in OpenFOAM (v1706 onwards), which possesses the potential to eliminate many barriers for the challenging dynamic mesh motion (DMM) in WEC simulations. This paper presents ongoing investigations considering the application of the overset method to a number of di cult to handle DMM scenarios which can be encountered in WEC NWT experiments. Read
Reviewing the literature of CFD-based numerical wave tanks for wave energy applications, it can be observed that different flow conditions and different turbulence models are applied during numerical wave energy converter (WEC) experiments. No single turbulence model can be identified as an `industry standard’ for WEC modeling. The complexity of the flow field around a WEC, together with the strong dependency of turbulence effects on the shape, operational conditions, and external forces, hampers the formulation of such an `industry standard’. Furthermore, the conceptually different flow characteristics (i.e., oscillating, free surface flows), compared to the design cases of most turbulence models (i.e., continuous single-phase flow), can be identified as a source for the potential lack of accuracy of turbulence models for WEC applications. This communication performs a first step towards analyzing the accuracy and necessity of modeling turbulence effects, by means of turbulence models, within CFD-based NWTs for WEC applications. To that end, the influence of turbulence models and, in addition, the influence of the initial turbulence intensity is investigated based on different wave–structure interaction cases considering two separately validated WEC models. The results highlight the complexity of such a `turbulence analysis’ and the study suggests specific future work to get a better understanding of the model requirements for the flow field around WECs
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Scaled model tests are an important step during the research and development of wave energy converters (WECs). While such scaled model tests in physical wave tanks are prone to undesired scaling effects due to e.g. mechanical artefacts and/or fluid effects, numerical wave tanks (NWTs) provide excellent tools for the analysis of WECs across a range of scales, overcoming the limitations of the physical test environment. Simultaneous scaling based on the Froude and Reynolds number is achievable in physical wave tanks only with significant effort, whereas NWTs allow the adjustment of fluid properties, such as viscosity, in an easy manner, thereby catering for Froude and Reynolds similarity. This study exploits the capabilities of a high-fidelity, computational fluid dynamics based, NWT and investigates the hydrodynamic scaling effects for the heaving buoy Wavestar WEC. Various test cases, relevant for WEC applications and with progressively increasing complexity, are considered to develop a comprehensive understanding of the scaling effects. Results show that significant scaling effects occur for the viscous component of the hydrodynamic loads on the WEC hull, while the system dynamics and total (viscous + pressure) loads are relatively unaffected by scaling effects. Read
This project has received funding from the European Union’s Horizon 2020
research and innovation programme