We present the treatment of lifting lines with a Vortex Particle-Mesh (VPM) methodology. The VPM method relies on the Lagrangian discretization of the Navier-Stokes equations in vorticity-velocity formulation. The use of this hybrid discretization offers several advantages. The particles are used solely for the advection, thereby waiving classical time stability constraints. They also exploit the compactness of vorticity support, leading to high computational gains for external flow simulations. The mesh, on the other hand, handles all the other computationally intensive tasks, such as the evaluation of the differential operators and the use of fast Fourier-based Poisson solvers, which allow the combination of unbounded directions and inlet/outlet boundaries. Both discretizations communicate through high order interpolation. The mesh and the interpolation also allow for additional advances; they are used to handle Lagrangian distortion by reinitializing the particle positions onto a regular grid. This crucial step, referred to as remeshing, guarantees the accuracy of the method. In addition, the resulting methodology provides computational efficiency and scalability to massively parallel architectures. Sources of vorticity are accounted for through a lifting line approach. This line handles the attached and shed vorticity contributions in a Lagrangian manner. Its immersed treatment efficiently captures the development of vorticity from thin sheets into a three-dimensional field. We apply this approach to the simulation of wake flows encountered in aeronautical and wind energy applications. An important aspect in these fields is the handling of turbulent inflows. We have developed a technique for the introduction of pre-computed or synthetic turbulent flow fields in vorticity form. Our treatment is based on particles as well and consistent with the Lagrangian character of the method. We apply here our method to the investigation of wind turbine wakes over very large distances, reaching cluster or wind farm sizes.

We develop a Vortex Particle-Mesh (VPM) method for the Large Eddy Simulation of wind turbine wakes and coarse scale aerodynamics.Based on the vorticity formulation of the Navier-Stokes equations, the approach combines the advantages of two discretizations. The particles handle the advection of vorticity, and exploit its compact support. The mesh is used for the evaluation of the differential operators and inside efficient Fourier-based Poisson solvers.The blades are modeled by means of lifting lines. This treatment is similar to a vortex lattice method, although it is here immersed in the mesh and allows the evolution of shed vorticity into a fully turbulent flow.We apply this tool to the investigation of atmospheric turbulence effects on the blade aerodynamics and on the wake behavior. To this end, the inflow boundary is feeding our VPM calculations with a turbulent vorticity field that has been computed in a preliminary LES of atmospheric turbulence.

We present the coupling of a vortex particle-mesh method with immersed lifting lines for the Large Eddy Simulation of wind turbine wakes. The method relies on the Lagrangian discretization of the Navier–Stokes equations in vorticity-velocity formulation. Advection is handled by the particles while the mesh allows the evaluation of the differential operators and the use of fast Poisson solvers. We use a Fourier-based fast Poisson solver which simultaneously allows unbounded directions and inlet/outlet boundaries. The method also allows the feeding of a turbulent incoming flow. We apply this methodology to the study of large scale aerodynamics and wake behavior of tandem wind turbines. We analyze the generators performance, unsteady power, loads and aerodynamics they are subjected to. The average flow field of the wakes is also computed and turbulence statistics are extracted. In particular, we investigate the influence of the type of turbulent inflow used—precomputed or synthetic—, and study wake meandering.

A Vortex Particle-Mesh (VPM) method with immersed lifting lines has been developed and validated. The vorticity-velocity formulation of the NS equations is treated in a hybrid way: particles handle advection while the mesh is used to evaluate the differential operators and for the fast Poisson solvers (here a Fourier-based solver which simultaneously allows for unbounded directions and inlet/outlet boundaries). Both discretizations communicate through high order interpolation. The immersed lifting lines handle the creation of vorticity from the blade elements and its early development. LES of Vertical Axis Wind Turbine (VAWT) flows are performed, with a relatively fine resolution (128 and 160 grid points per blade) and for computational domains extending up to 6D and 14D downstream of the rotor. The wake complex development is captured in details, from the blades to the near wake coherent vortices, to the transitional ones, to the fully developed turbulent far wake. Mean flow statistics in planes (horizontal, vertical and cross) are also presented. A case with a realistic turbulent wind inflow is also considered. The physics are more complex than for HAWT flows.

We present the coupling of a vortex particle-mesh method with immersed lifting lines. The method relies on the Lagrangian discretization of the Navier-Stokes equations in vorticity- velocity formulation. Advection is handled by the particles while the mesh allows the evaluation of the differential operators and the use of fast Poisson solvers. We use a Fourier-based fast Poisson solver which simultaneously allows unbounded directions and inlet/outlet boundaries. A lifting line approach models the vorticity sources in the flow. Its immersed treatment efficiently captures the development of vorticity from thin sheets into a three-dimensional field. We apply this approach to the simulation of a wind turbine wake at very high Reynolds number. The combined use of particles and multiscale subgrid models allows the capture of wake dynamics with minimal spurious diffusion and dispersion, while being computationally efficient.