###### Abstract
In such a context, the VAWT may be better suited to the emerging floating offshore market, as heavy components would all sit at the base of the turbine, and the rotor aerodynamics is less sensitive to wind skew and yaw with respect to HAWTs. VAWTs could thus potentially enhance the turbine performance and, at the same time, reduce the cost of FOWTs installation and maintenance, owing to the absence of high-speed shafts, yaw systems and nacelles which are all potentially subject to faults. In light of the renewed interest in VAWT technology in such emerging contexts, the development of accurate and effective tools for the prediction of VAWT performance and load are now of interest. The needs of future applications will involve to consider general rotor shapes, with special focus on the Troposkein shape (and its modifications) and considering the wind shear and skew which might be relevant, respectively, for mini-scale distributed applications and large-scale floating applications. To satisfy aforementioned requests, recent literature offers comprehensive BEM models, employing the Double Multiple Stream Tube approach, improved by analytical corrections as in [18; 29], implementing different models to correct incidence due to flow curvature, dynamic stall effects and streamtube expansion for H-shaped rotors. The main differences between the study by [PERSON] et al. and present 3D BEM code are that the former employs Prandtl-Lanchester correction to estimate performance losses at tips, the latter adopts [PERSON]'s tip losses correction adapted from HAWTs; regarding the dynamic stall model, results in [18] were obtained with [PERSON]'s model whereas this paper entails [PERSON]'s one. Both BEM codes envisage an extended polar database for accurate post- and deep-stall aerodynamic coefficients with smoothing and model strut and pole passive torque. Flow curvature is accounted for by [PERSON]'s virtual mapping method adding virtual incidence concept; only a simplistic correction by [PERSON] is chosen to correct the angles of attack in this work. On this point, [PERSON] et al. [29] developed a novel simple method to consider the 'decambering effect' of airfoil in cycloidal motion and compared results with already existent methods; the dynamic stall used is the Beddoes-Leishman and streamtube expansion model; however, passive torque corrections were not considered. The present paper documents the formulation, the validation and multiple applications of a novel BEM tool conceived to deal with 3D in-flow configurations coupled with 3D rotor architecture, and featuring 3D corrections to the base model considering the tip and strut loss contributions. The paper is structured as follows. At first the three exemplary VAWTs configurations used for validation and application purposes throughout the study are presented, then the novel BEM formulation model is described and its experimental validation is performed by resorting to wind-tunnel tests of the aforementioned VAWT prototypes. Then the BEM tool is applied to multiple case studies, at first comparingdifferent rotor architectures, rotor scales and blade profiles, and then considering exemplary on-shore installations in coastal regions and off-shore installations of the floating DeepWind turbine.