A prescribed velocity-vorticity boundary layer model for the vorticity transport equation is proposed, which corrects the unphysical upward deflection of the wake seen in a simpler prescribed velocity shear approach. A Lagrangian implementation of the boundary layer model has been investigated using our in-house vortex solver MIRAS. The MIRAS code contains both an aerodynamic part and a structural-mechanical part taking into account aeroelastic phenomena. The solver is employed to simulate flows around wind turbines and uses a combination of filaments and particles in order to mimic the vorticity released by the wind turbine blades. The vorticity is interpolated onto a uniform Cartesian mesh, where the interaction is efficiently calculated by an fast Fourier transform-based method. Simulations of wind turbines operating in an atmospheric boundary layer flow are carried out and analysed in detail for a range of scenarios. The manuscript focuses on studying the influence of wind shear and turbulence, which is varied to mimic natural atmospheric conditions. A traverse virtual probe up to 30 diameters downstream of the rotor plane is used to investigate the properties of the turbulent wake flow for the different cases.This includes mean and standard deviation of the streamwise velocity component, wake deficit, Reynolds stresses, and power spectral density of the velocity signal. The results show that combining a prescribed boundary layer approach with a vortex method gives consistent and physically correct results if properly implemented. KEYWORDS aeroelasticity, atmospheric boundary layer, turbulence, vortex method, wind shear, wind turbine INTRODUCTIONVortex methods initially entered the wind energy community as a more physically accurate alternative to the basic Blade Element Momentum method (BEM) technique, which is based on 1-dimensional momentum theory and aimed to be used for rotor design. However, vortex methods have quickly developed in recent years and now can be seen as an advanced and matured tool capable of performing high-fidelity simulations of 1 or more turbines. Vortex methods are not only of interest during the actual rotor design process but also as analysis tool to investigate more complex scenarios, including aeroelastic, turbulent inflow, and shear effects. [1][2][3][4][5][6] Vortex solvers can be combined with different aerodynamic models depending on the degree of complexity required. Enumerated in ascending complexity, they can be classified as lifting line (LL) vortex lattice, potential panel method, and viscous-inviscid panel method. The latter class being the more physically correct, since it resolves the actual geometry of the blade accounting for the viscous effects enclosed inside the boundary layer.The present paper focuses on the lower degree of fidelity in terms of aerodynamic modeling of the wind turbine blades, using the LL approach. With the LL model, the rotor blades are represented by discrete filaments, which account for the bound vortex strength and release vorticity into the ...

We present a Brinkman penalization method for three-dimensional (3D) flows using particle vortex methods, improving the existing technique by means of an iterative process. We perform simulations to study the impulsively started flow past a sphere at Re = 1000 and normal to a circular disc at Re = 500.The simulation results obtained for the flow past a sphere are found in qualitative good agreement with previously published results obtained using respectively a 3D vortex penalization method and a 3D vortex method combined with an accurate boundary element method. From the results obtained for the flow normal to a circular disc it is found that the iterative method enables the use of a time step that is one order of magnitude larger than required by the standard non-iterative Brinkman penalization method.

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