Folley, Matt

Silverthorne, Katherine

English

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Conference Paper, Published VersionSilverthorne, Katherine; Folley, MattWave farm energy yield calculations using a modifiedspectral wave modelZur Verfügung gestellt in Kooperation mit/Provided in Cooperation with:TELEMAC-MASCARET Core GroupVerfügbar unter/Available at: https://hdl.handle.net/20.500.11970/104300Vorgeschlagene Zitierweise/Suggested citation:Silverthorne, Katherine; Folley, Matt (2012): Wave farm energy yield calculations using amodified spectral wave model. In: Bourban, Sébastien; Durand, Noémie; Hervouet, Jean-Michel (Hg.): Proceedings of the XIXth TELEMAC-MASCARET UserConference 2012, 18 to 19 October 2012, St Hugh's College,Oxford. Oxfordshire: HR Wallingford. S. 159-164.Standardnutzungsbedingungen/Terms of Use:Die Dokumente in HENRY stehen unter der Creative Commons Lizenz CC BY 4.0, sofern keine abweichendenNutzungsbedingungen getroffen wurden. Damit ist sowohl die kommerzielle Nutzung als auch das Teilen, dieWeiterbearbeitung und Speicherung erlaubt. Das Verwenden und das Bearbeiten stehen unter der Bedingung derNamensnennung. Im Einzelfall kann eine restriktivere Lizenz gelten; dann gelten abweichend von den obigenNutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte.Documents in HENRY are made available under the Creative Commons License CC BY 4.0, if no other license isapplicable. Under CC BY 4.0 commercial use and sharing, remixing, transforming, and building upon the materialof the work is permitted. In some cases a different, more restrictive license may apply; if applicable the terms ofthe restrictive license will be binding.  Wave farm energy yield calculations using a modified spectral wave model  Katherine E. Silverthorne and Matt Folley School of Planning, Architecture, and Civil Engineering Queen’s University Belfast Belfast, Northern Ireland, UK k.silverthorne@qub.ac.uk    Abstract—The development and deployment of large arrays (100+ units) of wave energy converters (WECs) require numerical tools that support investigations into the potential effects of the wave farm deployment and make predictions about the wave farm’s annual energy production. Tools based on spectral wave models are particularly suited for this task because they can model large numbers of WECs with a lower computational effort than equivalent potential flow models, which are currently the most popular method. In this study, which was undertaken as part of PerAWaT (Performance Assessment of Wave and Tidal Array Systems) and commissioned and funded by the Energy Technologies Institute, a representation of a heaving buoy WEC is developed for the TOMAWAC spectral wave model. The representation solves the WEC dynamics using hydrodynamic coefficients from WAMIT and the incoming wave spectrum from TOMAWAC. The WEC response is then used to calculate the effect on the incident wave field. The results are compared with those from a potential flow model, followed by a discussion of the applications and limitations of the method. I. INTRODUCTION The wave energy industry has reached a stage in development where full scale devices are being built and deployed in ocean sites. Once the prototypes have been tested thoroughly, the next step in the process will be to deploy several devices together in an array in order to generate more power. Ultimately, tens to hundreds of devices will need to be deployed together in a wave farm in order to achieve the targets for marine renewable power production that have been set by UK government, [1]. Careful planning will be required before a wave farm is actually deployed. Once a potential site has been chosen, the development team must have an idea about the optimal arrangement of the array at that site, based on either minimizing negative array interactions or maximizing positive ones and taking into account any bathymetry or resource restrictions. The development team will also have to undertake an environmental impact assessment that predicts the effect of the array on the ocean waves (both close to the farm and further down wave near the coast) and any subsequent consequences of that impact on the sediment transport and ecology of the region where the farm is to be deployed. There are currently no available numerical tools that are capable of capturing both the propagation of waves and the behavior of hundreds of wave energy devices. Therefore, in order to perform pre-deployment assessment of a wave farm, a new numerical modeling tool is needed. The focus of this paper is on the development of just such a tool using the TOMAWAC model that is part of the TELEMAC suite of models developed at EDF, [2]. This work is part of the PerAWaT project (Performance Assessment of Wave and Tidal arrays) which incorporates several research organizations applying numerous numerical and experimental methods for estimation of wave energy farm array power production. There are several numerical modeling tools that are currently being used to model the interaction of wave energy devices and ocean surface waves, [3]. These include potential flow models (linear and nonlinear), Boussinesq wave models, time-domain models, spectral wave models, and computational fluid dynamics models. Potential flow models, time-domain models, and computational fluid dynamics models directly solve for the interaction of ocean waves with a wave energy device, while spectral wave models and Boussinesq wave models simulate the interaction of ocean waves with a parameterization of a wave energy device (i.e. the wave energy device is not explicitly represented). Because of the computational complexity involved in directly solving for the fluid-structure interaction, it is not feasible to simulate a wave farm with many devices in potential flow models, time-domain models, or CFD models. Spectral wave models are able to cover a larger domain area with a smaller computational load than Boussinesq wave models, and therefore are the best suited for simulation of wave farms. Spectral wave models were developed in the oceanography community for prediction of surface ocean waves. They solve a surface ocean wave energy conservation equation, and have the ability to represent several ocean wave processes as sinks or sources of energy, including whitecapping dissipation, bottom dissipation, bottom refraction, both quadruplet and triplet nonlinear wave-wave interactions, and wind generation. The ability of spectral wave models to include non-linear sources and sinks of wave energy indicates that it is also possible to incorporate non-linear wave energy device representations, [4]. Another advantage of using spectral wave models is that they can be used with a varying mesh size to cover large computational 159XIXth TELEMAC-MASCARET User Conference Oxford, UK, October 18–19, 2012    III. RESULTS A. Power absorption verification For each sea state, the power absorption was calculated for the same wave energy device in both the WAMIT and TOMAWAC models. The results for all the sea states show good agreement between the WAMIT and TOMAWAC calculated power absorption, with percent error differences of less than 2%, Table II. TABLE II.  POWER ABSORPTION COMPARISON Sea States TOMAWAC power absorbed (kW) WAMIT power absorbed (kW) % error SS1 9.7 9.8 -1.0 SS2 25.1 25.3 -0.8 SS3 65.8 67.1 -1.9 SS4 148.1 150.9 -1.9 SS5 25.4 25.0 1.6 SS6 150.1 149.0 0.7 SS7 25.4 25.0 1.6 SS8 150.1 149.0 0.7  B. Source term strength verification For each sea state and both the direct area method and the transmission coefficient method, the integrated flux and the power absorbed for the single wave energy device were calculated. The power absorbed by the device depends only on the incoming waves, and therefore does not change between methods. The results for this analysis are given in Table III. TABLE III.  SOURCE TERM STRENGTH METHOD COMPARISON Sea States Direct area method (kW) Trans-mission method (kW) Power absorbed (kW) % error: direct area method % error: trans-mission method SS1 13.6 34.8 9.7 40 258 SS2 35.5 72.9 25.1 41 190 SS3 93.1 140.7 65.8 41 114 SS4 209.5 316.6 148.1 41 114 SS5 36.3 74.6 25.4 43 194 SS6 214.3 323.9 150.1 43 116 SS7 35.0 71.9 25.4 39 185 SS8 206.7 312.5 150.1 38 109  IV. DISCUSSION While the calculation of the power absorption by the TOMAWAC model shows good agreement with the WAMIT model, it can be seen from Table III that neither of the source term strength conversion methods seems to give very good agreement between the power absorbed and the integrated energy flux. This indicates that both the methods tested for converting the power absorbed into a source term strength for the model are incorrect. However, the errors for the area method are close to 40% for all of the sea states, while the errors for the transmission coefficient method vary between 100% and 260%. This suggests that it may be possible to use one area for each mesh as in the direct area method, but that the value of the area used for the computation is incorrect. The “correct area” can be found iteratively by repeating the calculation using different areas until the power absorbed matches the integrated flux. This was tested on a series of different meshes, and the calibrated area was found to vary between 31% and 41% of the total area of the triangles surrounding the node where the wave energy device was located. Additionally, varying the main propagation direction of the ocean waves yields a different calibrated area for the same mesh. This suggests there is not a simple relationship between the size of the triangles surrounding the computational node and the correct area needed for the conversion. Instead, it seems there is a more complicated dependence, possibly involving the computational method. When the calibrated area is used, good agreement between the power absorbed and the integrated energy flux is found for all the sea states (Table IV): TABLE IV.  CALIBRATED AREA METHOD RESULTS Sea States Calibrated area method (kW) Power absorbed (kW) % error SS1 9.6 9.7 -1.0 SS2 24.9 25.1 -0.8 SS3 65.3 65.8 -0.8 SS4 147.0 148.1 -0.8 SS5 25.5 25.4 0.4 SS6 150.4 150.1 0.2 SS7 24.6 25.4 -2.8 SS8 145.1 150.1 -2.8  Furthermore, the distribution of the power absorbed and the integrated flux with frequency match very well, Fig. 4. This is further indication that it is correct to use a single area to define the conversion between the power absorbed and the wave energy density. It is therefore important to identify the dependence of the calibrated area on the computational parameters (including perhaps mesh size, time step, and others) so that a generic representation of many wave energy 163XIXth TELEMAC-MASCARET User Conference Oxford, UK, October 18–19, 2012    devices in the TOMAWAC model can be more easily implemented.  0.05 0.1 0.15 0.20510SS20.05 0.1 0.15 0.201020SS3Power absorbed (kW)0.05 0.1 0.15 0.202040SS40.05 0.1 0.15 0.20510SS50.05 0.1 0.15 0.202040SS60.05 0.1 0.15 0.20510SS7Frequency (Hz)0.05 0.1 0.15 0.202040SS8Frequency (Hz)0.05 0.1 0.15 0.2024SS1  Integrated fluxPower absorbed Figure 4.  Power absorbed and integrated flux as a function of frequency for 8 sea states using the calibrated area method. V. CONCLUSIONS It has been shown in this paper that it is possible to calculate the correct power absorption for a single wave energy device (as compared with the industry standard potential flow model WAMIT) and convert that power correctly to a source term strength in the spectral wave model TOMAWAC. However, the details of the conversion between power absorption and source term strength still need to be worked out. Now that progress has been made with simulating a single wave energy device, simulations of multiple devices can be considered. Multiple buoy simulations, as in a wave farm scenario, are more complicated because the phase-dependent wave processes such as diffraction around the buoys and radiation of waves away from the buoys are not explicitly resolved in spectral wave models. However it is expected that some of these effects may average out over a large array. In order to address these issues, the next phase of the research for development of a numerical tool that can model a wave farm will include comparison of the tool with both other numerical models and wave tank experimental data. This work is already underway as part of the PerAWaT project. ACKNOWLEDGEMENTS This work was undertaken as part of the PerAWaT (Performance Assessment of Wave and Tidal Array Systems) project that was commissioned by the Energy Technologies Institute. REFERENCES [1] Department of Energy and Climate Change, “ UK low carbon transition plan”, <http://www.decc.gov.uk/en/content/cms/tackling/ carbon_plan/lctl/lctp.aspx>, 2009. [2] M. Benoit, F. Marcos, and F. Becq, “Development of a third-generation shallow-water wave model with unstructured spatial meshing”, Proceedings of 25th International Conference on Coastal Engineering, 1996. [3] M. Folley et al., “A review of numerical modelling of wave energy converter arrays,” Proceedings of the ASME 2012 31st international conference on ocean, offshore, and Arctic engineering, June 10-15, 2012. [4] M.Folley and T. Whittaker, “Spectral modelling of wave energy converters”, Coastal Engineering, vol. 57, pp. 892-897, 2010. [5] D.L. Millar, H.C.M. Smith, and D.E. Reeve, “Modelling analysis of the sensitivity of shoreline change to a wave farm,” Ocean Engineering, vol. 34, pp. 884–901, 2006. [6] H.C.M Smith, C. Pearce, and D.L. Millar, “Further analysis of change in nearshore wave climate due to an offshore wave farm: An enhanced case study for the WaveHub site”, Renewable Energy, vol. 40, pp. 51-64, 2012. [7] A. Alexandre, T. Stallard, and P.K. Stansby, “Transformation of wave spectra across a line of wave devices”, Proceedings of 8th European wave and tidal energy conference, 2009. [8] K. E. Silverthorne and M. Folley, “A new numerical representation of wave energy converters in a spectral wave model”, Proceedings of 9th European wave and tidal energy conference, 2011. [9] A. Alexandre, T. Stallard, and P.K. Stansby, “Wavefield modification due to a WEC array”, Proceedings of third international conference on the application of physical modelling to port and coastal protection, 2010.  164

Wave farm energy yield calculations using a modified spectral wave model

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Wave farm energy yield calculations using a modified spectral wave model

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