High Order CFD

highCFD_IITidal turbines share some of their fluid dynamic characteristics with their close relatives wind turbines. Among others 3D effects (e.g. tip and root effects) and the relative movement of the blades to the fixed environment leading to  rotational effects (i.e. existence of centripetal and Coriolis forces modifying the flow characteristics) are of importance in this type of power generation device. The environments in which wind and tidal turbines operate share some similarities, both environments experience high levels of turbulence with eddies of variable size and shape, and thick boundary layers shaping the incoming flow.

However, certain environmental conditions are characteristic of the tidal environment. The presence of the free surface, its confining effect and its deformation due to the energy extracted by marine turbines, are the main differences between air and water power generation technologies.

Esteban_IIThe objective of this project is to simulate the different flow physics involved in tidal power generation using high order discontinuous Galerkin finite element methods (DG-FEM). To this end the DG@Tidal code is under development.

The method allows for the accurate simulation of rotating blades under high Reynolds number conditions. The prediction of freestream turbulence and vortex shedding on the turbine efficiency and blade hydrodynamics is to be characterised. Tidal turbine wakes and their dependency on incoming turbulent structures will also be investigated.

The DG_FEM method can be defined as an extension of Spectral h/p methods where the C0 continuity requirement across element boundaries is relaxed or as a high order Finite Volume method. As in Spectral methods,  high-order polynomials can be used within each element allowing for exponential convergence. However, in DG methods continuity is not required and therefore different polynomial orders can be easily used in different elements. 



Moreover, if hanging nodes are used, as are required for sliding mesh interfaces as would occur in tidal turbine simulations, the DG method provides a natural advantage as the discontinuities can be naturally handled. Another advantage of DG methods, over continuous FE, is that, as for the FV method, the local conservation of flow properties are explicitly ensured in an element fashion by the numerical fluxes.
High order DG-FEM offer high flexibility since h-refinement (mesh size refinement) and p-refinement (polynomial expansion refinement) can be performed independently. This flexibility is advantageous when simulating flows that have very different characteristic sizes throughout the domain (e.g. blade hydrodynamics versus turbine wake).