SUMMARYThis paper focuses on the assessment of a discontinuous Galerkin method for the simulation of vortical flows at high Reynolds number. The Taylor–Green vortex at Re = 1600 is considered. The results are compared with those obtained using a pseudo‐spectral solver, converged on a 5123 grid and taken as the reference. The temporal evolution of the dissipation rate, visualisations of the vortical structures and the kinetic energy spectrum at the instant of maximal dissipation are compared to assess the results. At an effective resolution of 2883, the fourth‐order accurate discontinuous Galerkin method (DGM) solution (p = 3) is already very close to the pseudo‐spectral reference; the error on the dissipation rate is then essentially less than a percent, and the vorticity contours at times around the dissipation peak overlap everywhere. At a resolution of 3843, the solutions are indistinguishable. Then, an order convergence study is performed on the slightly under‐resolved grid (resolution of 1923). From the fourth order, the decrease of the error is no longer significant when going to a higher order. The fourth‐order DGM is also compared with an energy conserving fourth‐order finite difference method (FD4). The results show that, for the same number of DOF and the same order of accuracy, the errors of the DGM computation are significantly smaller. In particular, it takes 7683 DOF to converge the FD4 solution. Finally, the method is also successfully applied on unstructured high quality meshes. It is found that the dissipation rate captured is not significantly impacted by the element type. However, the element type impacts the energy spectrum in the large wavenumber range and thus the small vortical structures. In particular, at the same resolution, the results obtained using a tetrahedral mesh are much noisier than those obtained using a hexahedral mesh. Those obtained using a prismatic mesh are already much better, yet still slightly noisier. Copyright © 2013 John Wiley & Sons, Ltd.

This work aims at assessing the performance of a tip‐loss correction for advanced actuator disk (AD) methods coupled to large eddy simulation and making this correction possible in a wind farm configuration. The classical Glauert tip‐loss factor, commonly used in the blade element momentum method, is added here to correct the tip and the root induced velocities at the rotor. However, it requires a reference upstream velocity, which is problematic to define in complex flows, such as in wind farms. A methodology is proposed here to infer an effective upstream velocity local to each disk element, based on the one‐dimensional momentum theory and using only the local data at the rotor. This estimation is verified through a set of simulations, leading to good results in spite of the crude assumptions of the one‐dimensional momentum theory. This AD supplemented with the tip‐loss correction is compared with a high fidelity vortex particle‐mesh method, through the simulations in uniform wind of a constant circulation wind turbine and of a more realistic machine, the NREL‐5MW rotor. The results show that the AD behavior is clearly improved by the addition of a tip‐loss factor and the potential errors on the effective upstream velocity estimation have a moderate impact on the tip‐loss correction.

This study is concerned with the investigation of two-vortex systems (2VS) of various strengths that are released near the ground and evolve in the presence of a turbulent crosswind. We analyze the physics of the vortices interactions with the turbulent wind and with the ground during the rebound phase, and that lead to the fully developed turbulent flow and interactions. The transport and decay of the vortices are also analyzed. The turbulent wind itself is obtained by direct numerical simulation using a half channel flow. The flow is then supplemented with the 2VS, using vortices with a circulation distribution that is representative of vortices after roll-up of a near wake. The vortex strengths, Γ0, are such that ReΓ = Γ0/ν = 2.0 × 104 for the baseline; there is then a case with twice weaker vortices, and a case with twice stronger vortices. The simulations are run in wall-resolved Large Eddy Simulation (LES) mode. The baseline is in line with the wall-resolved LES study of a similar case [A. Stephan et al., “Aircraft wake-vortex decay in ground proximity—Physical mechanisms and artificial enhancement,” J. Aircr. 50(4), 1250–1260 (2013)]. They highlighted the significant effect that the near-wall streaks of the wind have on the development of instabilities in the secondary vortices, and the ensuing turbulence. Our analysis complements theirs by also showing the significant effect that the wind turbulent structures, away from the ground and that are stretched by the primary vortices, also have on the destabilization of the secondary vortices. Comparisons are also made with the most recent study [F. N. Holzäpfel et al., “Wind impact on single vortices and counter-rotating vortex pairs in ground proximity,” in 7th AIAA Atmospheric and Space Environments Conference, AIAA Aviation (American Institute of Aeronautics and Astronautics, 2015)], where ReΓ = 2.0 × 104 for all cases and where it is the wind intensity that is varied. Diagnostics on the vortex trajectories and circulation decay are provided, for the mean and for the envelopes of behaviour. The results are discussed and compared with the recent literature. In particular, for the case with relatively twice stronger wind relative to the vortices, the upwind vortex quickly looses its coherence when it comes closest to the ground and does not rebound; the physics of that are explained by a long wave instability excited by the turbulent wind. Finally, a case where the baseline wake is released at a lower altitude is also studied, to support an analysis on what is the proper length scale to use, and initial time, when comparing results of wakes released at different altitudes: indeed, when normalized using those quantities, the trajectory and decay curves of this case are seen to collapse very well with those of the baseline.

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Abstract.A vortex particle-mesh (VPM) method with immersed lifting lines has been developed and validated. Based on the vorticity-velocity formulation of the Navier-Stokes equations, it combines the advantages of a particle method and of a mesh-based approach. The immersed lifting lines handle the creation of vorticity from the blade elements and its early development. Large-eddy simulation (LES) of vertical axis wind turbine (VAWT) flows is performed. The complex wake development is captured in detail and over up to 15 diameters downstream: from the blades to the near-wake coherent vortices and then through the transitional ones to the fully developed turbulent far wake (beyond 10 rotor diameters). The statistics and topology of the mean flow are studied. The computational sizes also allow insights into the detailed unsteady vortex dynamics and topological flow features, such as a recirculation region influenced by the tip speed ratio and the rotor geometry.