A correction to the enhanced bottom drag parameterisation of tidal turbines

Hydrodynamic modelling is an important tool for the development of tidal stream energy projects. Many hydrodynamic models incorporate the effect of tidal turbines through an enhanced bottom drag. In this paper we show that although for coarse grid resolutions (kilometre scale) the resulting force exerted on the flow agrees well with the theoretical value, the force starts decreasing with decreasing grid sizes when these become smaller than the length scale of the wake recovery. This is because the assumption that the upstream velocity can be approximated by the local model velocity, is no longer valid. Using linear momentum actuator disc theory however, we derive a relationship between these two velocities and formulate a correction to the enhanced bottom drag formulation that consistently applies a force that remains closed to the theoretical value, for all grid sizes down to the turbine scale. In addition, a better understanding of the relation between the model, upstream, and actual turbine velocity, as predicted by actuator disc theory, leads to an improved estimate of the usefully extractable energy. We show how the corrections can be applied (demonstrated here for the models MIKE 21 and Fluidity) by a simple modification of the drag coefficient

Turbulence-resolving simulations of wind turbine wakes

Turbulence-resolving simulations of wind turbine wakes are presented using a high--order flow solver combined with both a standard and a novel dynamic implicit spectral vanishing viscosity (iSVV and dynamic iSVV) model to account for subgrid-scale (SGS) stresses. The numerical solutions are compared against wind tunnel measurements, which include mean velocity and turbulent intensity profiles, as well as integral rotor quantities such as power and thrust coefficients. For the standard (also termed static) case the magnitude of the spectral vanishing viscosity is selected via a heuristic analysis of the wake statistics, while in the case of the dynamic model the magnitude is adjusted both in space and time at each time step. The study focuses on examining the ability of the two approaches, standard (static) and dynamic, to accurately capture the wake features, both qualitatively and quantitatively. The results suggest that the static method can become over-dissipative when the magnitude of the spectral viscosity is increased, while the dynamic approach which adjusts the magnitude of dissipation locally is shown to be more appropriate for a non-homogeneous flow such that of a wind turbine wake

Integrating Research Data Management into Geographical Information Systems

Ocean modelling requires the production of high-fidelity computational meshes upon which to solve the equations of motion. The production of such meshes by hand is often infeasible, considering the complexity of the bathymetry and coastlines. The use of Geographical Information Systems (GIS) is therefore a key component to discretising the region of interest and producing a mesh appropriate to resolve the dynamics. However, all data associated with the production of a mesh must be provided in order to contribute to the overall recomputability of the subsequent simulation. This work presents the integration of research data management in QMesh, a tool for generating meshes using GIS. The tool uses the PyRDM library to provide a quick and easy way for scientists to publish meshes, and all data required to regenerate them, to persistent online repositories. These repositories are assigned unique identifiers to enable proper citation of the meshes in journal articles.Comment: Accepted, camera-ready version. To appear in the Proceedings of the 5th International Workshop on Semantic Digital Archives (http://sda2015.dke-research.de/), held in Pozna\'n, Poland on 18 September 2015 as part of the 19th International Conference on Theory and Practice of Digital Libraries (http://tpdl2015.info/

Utilising the flexible generation potential of tidal range power plants to optimise economic value

Tidal range renewable power plants have the capacity to deliver predictable energy to the electricity grid, subject to the known variability of the tides. Tidal power plants inherently feature advantages that characterise hydro-power more generally, including a lifetime exceeding alternative renewable energy technologies and relatively low Operation & Maintenance costs. Nevertheless, the technology is typically inhibited by the significant upfront investment associated with capital costs. A key aspect that makes the technology stand out relative to other renewable options is the partial flexibility it possesses over the timing of power generation. In this study we provide details on a design methodology targeted at the optimisation of the temporal operation of a tidal range energy structure, specifically the Swansea Bay tidal lagoon that has been proposed within the Bristol Channel, UK. Apart from concentrating on the classical incentive of maximising energy, we formulate an objective functional in a manner that promotes the maximisation of income for the scheme from the Day-Ahead energy market. Simulation results demonstrate that there are opportunities to exploit the predictability of the tides and flexibility over the precise timing of power generation to incur a noticeable reduction in the subsidy costs that are often negotiated with regulators and governments. Additionally, we suggest that this approach should enable tidal range energy to play a more active role in ensuring security of supply in the UK. This is accentuated by the income-based optimisation controls that deliver on average more power over periods when demand is higher. For the Swansea Bay tidal lagoon case study a 23% increase is observed in the income obtained following the optimisation of its operation compared to a non-adaptive operation. Similarly, a 10% increase relative to an energy-maximisation approach over a year’s operation suggests that simply maximising energy generation in a setting where power prices vary may not be an optimal strategy

E2N: Error Estimation Networks for Goal-Oriented Mesh Adaptation

Given a partial differential equation (PDE), goal-oriented error estimation allows us to understand how errors in a diagnostic quantity of interest (QoI), or goal, occur and accumulate in a numerical approximation, for example using the finite element method. By decomposing the error estimates into contributions from individual elements, it is possible to formulate adaptation methods, which modify the mesh with the objective of minimising the resulting QoI error. However, the standard error estimate formulation involves the true adjoint solution, which is unknown in practice. As such, it is common practice to approximate it with an 'enriched' approximation (e.g. in a higher order space or on a refined mesh). Doing so generally results in a significant increase in computational cost, which can be a bottleneck compromising the competitiveness of (goal-oriented) adaptive simulations. The central idea of this paper is to develop a "data-driven" goal-oriented mesh adaptation approach through the selective replacement of the expensive error estimation step with an appropriately configured and trained neural network. In doing so, the error estimator may be obtained without even constructing the enriched spaces. An element-by-element construction is employed here, whereby local values of various parameters related to the mesh geometry and underlying problem physics are taken as inputs, and the corresponding contribution to the error estimator is taken as output. We demonstrate that this approach is able to obtain the same accuracy with a reduced computational cost, for adaptive mesh test cases related to flow around tidal turbines, which interact via their downstream wakes, and where the overall power output of the farm is taken as the QoI. Moreover, we demonstrate that the element-by-element approach implies reasonably low training costs.Comment: 27 pages, 14 figure