A row of wind turbine rotors with a mutual spacing of three diameters is simulated using both Reynolds averaged Navier-Stokes (RANS) simulations and a simple inviscid vortex model. The angle between the incoming wind and the line connecting the turbines is varied between 45 and 90 degrees. The simulations show that the power production of the turbines deviate significantly compared with a corresponding isolated turbine even though there is no direct wake-turbine interaction at the considered wind directions. Nevertheless, both models indicate marked alterations in the upstream flow, which directly link to the turbines' power adjustments. Thus, turbines which are placed laterally relative to the prevailing wind (as seen at various test sites) have, at least numerically, a mutual effect on each other. Therefore, they might not necessarily produce the same power as a stand-alone turbine.

Wind farm blockage effects are currently neglected in the prediction of wind farm energy yield, typically leading to an overestimation of the production. This work presents a novel method to assess wind farm production, while accounting for blockage effects. We apply a vortex model, based on a cylindrical wake, to assess induction effects. We present variations of the model to account for finite wake length, finite tip-speed ratios, and the proximity to the ground. The results are applied to single rotors in aligned and yawed conditions and to different wind farm layouts. We provide far-field approximations for faster estimates of the velocity field. Further, this article includes a new methodology to couple the induction model to engineering wake models, such as the ones present in the FLOw Redirection and Induction in Steady State (FLORIS). We compare the results to actuator disk simulations for various operating conditions of a single turbine and different wind farm layouts. We found that the mean relative error of the model in the induction zone is typically around 0.2% compared with actuator disk simulations. The computational time of the velocity field using the analytical vortex model is three orders of magnitude less than the one obtained with the actuator disk simulation.

The induction zone in front of different wind turbine rotors is studied by means of steady‐state Navier‐Stokes simulations combined with an actuator disk approach. It is shown that, for distances beyond 1 rotor radius upstream of the rotors, the induced velocity is self‐similar and independent of the rotor geometry. On the basis of these findings, a simple analytical model of the induction zone of wind turbines is proposed.

Abstract. The actuator line (AL) was intended as a lifting line (LL) technique for computational fluid dynamics (CFD) applications. In this paper we prove – theoretically and practically – that smearing the forces of the actuator line in the flow domain forms a viscous core in the bound and shed vorticity of the line. By combining a near-wake representation of the trailed vorticity with a viscous vortex core model, the missing induction from the smeared velocity is recovered. This novel dynamic smearing correction is verified for basic wing test cases and rotor simulations of a multimegawatt turbine. The latter cover the entire operational wind speed range as well as yaw, strong turbulence and pitch step cases. The correction is validated with lifting line simulations with and without viscous core, which are representative of an actuator line without and with smearing correction, respectively. The dynamic smearing correction makes the actuator line effectively act as a lifting line, as it was originally intended.

The actuator line was intended as a lifting line technique for CFD applications. In this paper we proof -theoretically and practically -that smearing the forces of the actuator line in the flow domain necessarily leads to smeared velocity fields. By combining a near-wake representation of the trailed vorticity with a viscous vortex core model, the missing induction from the smeared velocity is recovered. This novel dynamic smearing correction is verified for basic wing test cases and rotor simulations of a multi-MW turbine. The latter cover the entire operational wind speed range as well as yaw, strong turbulence and pitch 5 step cases. The correction is validated with lifting line simulations with and without viscous core, that are representative of an actuator line without and with smearing correction, respectively. The dynamic smearing correction makes the actuator line effectively act as a lifitng line, as it was originally intended. 10 The actuator line (AL) technique developed by Sørensen and Shen (2002) is a lifting-line (LL) representation of the wind turbine rotor suitable for computational fluid dynamics (CFD) simulations. It captures transient physical features like shed and trailed vorticity (including root/tip vortices) , without the computational cost associated with resolving the full rotor geometry. The AL model thus enables Large-eddy simulations (LES) of large wind farms in realistic, turbulent atmospheric boundary layers (Vollmer et al., 2017).15However, different to LL vortex formulations the blade forces are dispersed in the flow domain -most commonly in form of a Gaussian projection -to avoid numerical instability. A length scale -also referred to as smearing factor -controls this force redistribution, whose lower limit is linked to the grid size through numerical stability requirements (Troldborg et al., 2009). Mikkelsen (2003 observed a large sensitivity of the blade velocities to this length scale, which consequently also propagated to the blade forces. Especially in regions along the blade exhibiting stark load changes, as around the root and tip, forces 20 are substantially over-predicted. Meaning this effect is exacerbated by non-tapered and low aspect ratio blades. As actuator disc formulations suffer from similar issues towards the blade tip, their Glauert (1935) type tip corrections are also frequently applied to ALs (Shen et al., 2005). Yet, these correct discs for missing discrete blades and thus should be unnecessary -strictly even invalid -for ALs. Shives and Crawford (2013) and Jha et al. (2014) achieved a reduction in the force over-prediction Wind Energ. Sci. Discuss., https://doi.