Abstracts

Courses and hand-on sessions

John Ringwood, Maynooth University, Irlande

Hydrodynamic parameter fitting using the FOAMM toolbox

The use of boundary element tools such as WAMIT, Nemoh, etc are ubiquitous in hydrodynamic modelling for wave energy systems. However, usually, the frequency domain data returned by such utilities is in nonparametric from, which is difficult to deal with from a simulation (requiring convolution calculations) or a control perspective, where a parametric model form is mandatory. Recently, to complement the range of available parametric modelling tools, the Centre for Ocean Energy Research (COER) has developed the FOAMM toolbox, based on moment matching. The moment matching approach has several appealing characteristics, including the ability to match at specific user-defined frequencies, a monotonically decreasing fitting error (with increasing model order), a realisation that can be forced to be passive, and a significant computational cost saving for arrays of WECs. The session will involve a brief presentation of the FOAMM toolbox, and the theory upon which it is based, as well as an application example. Following the presentation, participants will have the opportunity to have a hands-on session with the FOAMM toolbox. For this session, an application example will be provided, but participants are also encouraged to bring hydrodynamic data of their own generated by Nemoh or WAMIT. For reference, the FOAMM toolbox is freely available at:

http://www.eeng.nuim.ie/coer/downloads/

Further information on the FOAMM toolbox in:

1. Faedo, N., Pena-Sanchez and Ringwood, J.V. Finite-order hydrodynamic model determination for wave energy applications using moment matching, Ocean Engineering, Vol.163, pp 251-263, 2018. [Link to PDF]
2. Pena-Sanchez, Y., Faedo, N. and Ringwood, J.V. Hydrodynamic model fitting for wave energy applications using moment matching: A case study, Proc. 28^th Intl. Conference on Ocean and Polar Engineering (ISOPE), Sapporo, Japan, pp 641-648, June 2018. [Link to PDF]
3. Faedo, N., Peña-Sanchez, Y. and Ringwood, J.V. Moment-Matching-Based Identification of Wave Energy Converters: the ISWEC Device, Proc. 11th IFAC Conference on Control Applications in Marine Systems, Robotics, and Vehicles (CAMS), Opatija, Croatia, Sept. 2018, pp 189-194. [Link to PDF]
4. Faedo, N., Pena-Sanchez, Y. and Ringwood, J.V. Passivity preserving moment-based finite-order hydrodynamic model identification for wave energy applications, Proc. RENEW 2018, Lisbon, pp 351-359, Oct. 2018. [Link to PDF]

Claes Eskilsson (Aalbord University) and David Lannes (U. Bordeaux)

Hierarchy of models for waves structure interaction (course)

Maria Kazolea (INRIA) and L. Weynans (U. Bordeaux)

Numerical implemantation of boundary conditions in long waves models (hands on session)

During the course we will survey different approaches to describe fluid-structure interactions, starting from the Navier-Stokes and Euler equations, fully nonlinear potential models, and describing also a general approach to derive simpler models based on shallow water asymptotic equations (nonlinear shallow water equations, Boussinesq and Green-Naghdi systems). For models that include dispersion, this latter approach requires to solve initial boundary value problems which are challenging, both theoretically and numerically. The hands on session will be devoted to the numerical study and comparisan of several techniques to handle the presence of a boundary in such problems.

Long talks

Emiliano Renzi, Loughborough University, Mathematical Sciences

Wave energy systems modelling – the case of the oscillating wave surge converter

The Oscillating Wave Surge Converter (OWSC) is a flap-type device that extracts energy by oscillating as an inverted pendulum under the action of incident waves. In this talk, I will discuss the hydrodynamic behaviour and performance of the OWSC, stemming from almost a decade of research in the hydrodynamic modelling of wave energy converters. I will start by discussing the behaviour of a single device in a linearised context, and then explore the dynamics of arrays and large wave farms. I will then move to the weakly nonlinear regime by showing some interesting resonant effects of an array of closely interacting gates. Finally, I will show some recent results to characterise the maximum wave load in extremely nonlinear slamming events.

Peter Stansby, School of Mechanical, Aerospace and Civil Engineering, University of Manchester

Linear diffraction modelling for multi-float platforms for wind and wave energy: from operational to extreme waves

Linear diffraction/radiation modelling has been a mainstay in offshore engineering for many years and is now being applied to multi-float platforms for wind and wave energy.  Time stepping formulations are desirable for nonlinear effects due to drag, moorings, power take off for wave energy and aerodynamic loads for wind energy.  Excitation, radiation damping and added mass force coefficients may be obtained from potential-flow panel codes such as WAMIT and included in a multi-body formulation. Second-order forces for fixed bodies may be added giving mean loads but mean loads due to body motion causing energy flux absorption from radiation, drag, and mechanical damping have not been accounted for although they have been in frequency-domain analyses. A time-stepping multi-body formulation is presented including these additional effects.  Wave basin measurements have been made for the multi-float wave energy converter M4 (with 6 floats) and an idealised 4-float semi-submersible wind platform with damping plates. Wave conditions were varied from operational (with H_s around 2 m at full scale) to extreme. The mooring was through a simple single-point buoy which is fully coupled in the multi-body model. The response of the floats is well predicted in operational but also surprisingly in extreme conditions with appropriate drag coefficients. The power prediction for wave energy was slightly underestimated, also surprisingly. The mean mooring forces for large waves were however underestimated markedly (equal to the mean hydrodynamic input force). With the experimentally measured mean forces input the peak mooring forces were predicted reasonably with appropriate drag and damping coefficients although values were quite sensitive to these values.  The float responses were effectively uncoupled from the mooring forces and some spectra will be shown. The biggest uncertainty appears to be in the mean forces and possible origins will be suggested. Such computational methods are quite efficient with run times of order one minute on a laptop (although hydrodynamic coefficients take much longer) compared with CFD run times of order one day on multi-processors. The sensitivity of mooring force to drag coefficient does suggest that CFD results will be sensitive to mesh resolution which determines boundary layer formation and separation. Fully converged CFD results may be problematic.

Invited talks

Josh Davidson, Budapest University of Technology and Economics, Department of Fluid Mechanics

Nonlinear Rock and Roll - Modelling and control of parametric resonance in WECs

Parametric resonance is a nonlinear phenomenon caused by the time-varying changes in the parameters of a system. Whereas normal resonance cause oscillations in a system to grow linearly with time, parametric resonance cause an exponential increase in oscillation amplitude. Parametric resonance has been observed in floating bodies, dating back to Froude in 1861, who described “large roll motion of ships occur when the roll natural period is approximately double the heave or pitch natural period”- Nonlinear Rock and Roll.

The concept of resonance is well known in the study of wave energy converters (WECs), with the natural frequency of WECs typically designed to resonate with the external excitation provided by the input wave field. Parametric resonance, on the other hand, has received very little attention, likely due to the complexity of the models required to capture this nonlinear phenomenom, compared to the traditional linear/frequency domain models favoured in WEC research and analysis. This presentation examines the modeling methods available for simulating, analysing and controlling parametric resonances in WECs. The traditional linear hydrodynamic models are discussed and contrasted against nonlinear hydrodynamic modelling approaches, in terms of model fidelity and computational requirements.

Adi Kurniawan, Aalborg University, Danmark

Wave energy absorption using flexible air-filled bags

The search for an economic means to harness energy from ocean waves continues. This talk summarizes recent studies of novel wave energy devices in which flexible, deformable, structures are used instead of conventional rigid structures. Each device utilizes a flexible air-filled bag, in the form of a fabric encased within an array of meridional tendons, to capture energy from the waves. Expansion and contraction of the bag in waves create a reciprocating air flow via a turbine between the bag and another volume. A series of model tests at approximately 1:20 scale was conducted to investigate the static behaviour of the bags in still water and their dynamic response in waves. For each device, numerical models are also developed based on linear potential theory and generalized modes approach to model the deformation of the tendons. The numerical predictions are generally in good agreement with the measurements. Both reveal some interesting properties that are distinct from one device configuration to another.

Kourosh Rezanejad, University of Lisbon, Centre for Marine Technology and Ocean Engineering (CENTEC)

Hydrodynamic Analysis and Optimization of Oscillating Water Column Wave Energy Converters

The beneficial effects of designing an oscillating water column (OWC) wave energy converter (WEC) by associating the hydrodynamics of the oscillating water masses to a dual-mass systems will be presented. The primary efficiency of a simple one degree of freedom WEC as well as a dual-mass WEC concept will be derived analytically for shallow water waves. It will be shown that substantial improvements in primary efficiency bandwidth could be reached by the application of the dual-mass concept. The primary efficiency of an OWC device deployed on stepped sea bottom will be discussed based on both numerical and experimental approaches, as an example of a dual-mass system. 

John Ringwood, Maynooth University, Irlande

An overview of wave energy control systems

This talk will explore the benefits of utilising energy-maximising control in conjunction with wave energy converters (WECs). The basics of impedance matching control for linear WEC models will be covered, while the latter part of the presentation will explore more powerful real-time WEC control schemes which can work well in irregular waves, observe any physical system constraints and, in some cases, deal with nonlinear WEC system models. High-performance WEC controllers also require access to an excitation force estimate, which can be provided by a state estimator and, due to the non causal nature of the WEC control problem, future values of excitation force are required. Both these issues will be covered in the talk. In addition, the extension of WEC control (and estimation and forecasting) to wave energy device arrays will also be dealt with.

Useful background:

1. Korde, U. A., & Ringwood, J. Hydrodynamic control of wave energy devices. Cambridge University Press, 2016.
2. Ringwood, J.V., Bacelli, G. and Fusco, F. Energy maximising control of wave energy converters, IEEE Control Systems Magazine, Vol.34, No.5, Oct. 2014, pp 30-55. [Link to PDF]

Short talks

Simone Michele, Loughborough University, UK

Weakly nonlinear theory of an array of curved wave energy converters

The nonlinear behaviour of an array of curved gate-type wave energy converters (WECs) in a semi-infinite channel of constant depth is analysed. Gate-type WECs have attracted interests by researchers and industry, mainly because of their capability to absorb energy with potentially large efficiency when excited by incident waves. However, the vast majority of the theoretical models developed so far on the dynamics of gate-type WECs neglect nonlinear contributions. This can be unjustified when nonlinear resonances of trapped modes occur. Indeed, Michele et al. (2018) recently showed that subharmonic resonance and mode competition of trapped modes can increase energy production of a system of gate-type WECs.
Moreover, recent investigations on curved flap-type gates suggest that using curved structures could further improve wave energy extraction efficiency. Motivated by these new aspects, in this work we investigate the effect of gate surface curvature on the nonlinear dynamics of an array of surging WECs.
It is shown that a small horizontal deviation of the gate surface produces significant changes in the dynamical behaviour of the system. Using perturbation-harmonic expansion up to the third order, the nonlinear governing equations is decomposed in a sequence of linearised boundary-value problems of order n and harmonic m. The gate shape effects resonate the first harmonic at the second order, so that three timing with two slow time scales is necessary.
First, we analyse the occurrence of synchronous nonlinear resonance by monochromatic incident waves with constant small amplitude and frequency equal to the eigenfrequency of the array. Products between the gate shape function and the second-order terms force the first harmonic at the third order. Perturbation expansion of the unknowns gives new terms in the Ginzburg-Landau evolution equation, which are not present in the case of flat gates.
This particular excitation is not possible for flat gates, because in that case the corresponding evolution equation would be damped and unforced. We show that this synchronous resonance can be substantial for design purposes.
Finally, we consider the subharmonic excitation of a single mode. Using action-angle variables, we analyse the occurrence of stable and unstable branches for the fixed points.
Then an optimized PTO coecient which maximises power extraction under subharmonic resonance is found. The capture factor reaches much larger values than the theoretical maximum of a WEC in a channel described by the linearised theory. Furthermore, we show that subharmonic resonance is associated with increased eciency of wave power extraction, though the effects of curvature are not always beneficial as we initially thought.