Abstract. We show that the upscaling of wind turbines from rotor diameters of 15–20 m to presently large rotors of 150–200 m has changed the requirements for the aerodynamic blade element momentum (BEM) models in the aeroelastic codes. This is because the typical scales in the inflow turbulence are now comparable with the rotor diameter of the large turbines. Therefore, the spectrum of the incoming turbulence relative to the rotating blade has increased energy content on 1P, 2P, …, nP, and the annular mean induction approach in a classical BEM implementation might no longer be a good approximation for large rotors. We present a complete BEM implementation on a polar grid that models the induction response to the considerable 1P, 2P, …, nP inflow variations, including models for yawed inflow, dynamic inflow and radial induction. At each time step, in an aeroelastic simulation, the induction derived from a local BEM approach is updated at all the stationary grid points covering the swept area so the model can be characterized as an engineering actuator disk (AD) solution. The induction at each grid point varies slowly in time due to the dynamic inflow filter but the rotating blade now samples the induction field; as a result, the induction seen from the blade is highly unsteady and has a spectrum with distinct 1P, 2P, …, nP peaks. The load impact mechanism from this unsteady induction is analyzed and it is found that the load impact strongly depends on the turbine design and operating conditions. For operation at low to medium thrust coefficients (conventional turbines at above rated wind speed or low induction turbines in the whole operating range), it is found that the grid BEM gives typically 8 %–10 % lower 1 Hz blade root flapwise fatigue loads than the classical annular mean BEM approach. At high thrust coefficients that can occur at low wind speeds, the grid BEM can give slightly increased fatigue loads. In the paper, the implementation of the grid-based BEM is described in detail, and finally several validation cases are presented. Comparisons with blade loads from full rotor CFD, wind tunnel experiments and a field experiment show that the model can predict the aerodynamic forces in half-wake, yawed flow, dynamic inflow and turbulent inflow conditions.

In this paper, an aerodynamic model consisting of a lifting line-based trailed vorticity model and a blade element momentum (BEM) model is described. The focus is on the trailed vorticity model, which is based on the near wake model (NWM) by Beddoes and has been extended to include the effects of downwind convection and to enable a faster and more accurate computation of the induction, especially close to the blade root and tip. The NWM is introduced to model the detailed steady and unsteady induction from the first part of the trailed vorticity behind the individual rotor blades. The model adds a radial coupling between the blade sections and provides a computation of tip loss effects that depends on the actual blade geometry and the respective operating point. Moreover, the coupling of the NWM with a BEM theory-based far wake model is presented. To avoid accounting for the near wake induction twice, the induction from the BEM model is reduced by a coupling factor, which is continuously updated during the computation to ensure a good behavior of the model in varying operating conditions. The coupled near and far wake model is compared with a simple prescribed wake lifting line model, a BEM model and full rotor computational fluid dynamics (CFD) to evaluate the steady-state results in different cases. The model is shown to deliver good results across the whole operation range of the NREL 5-MW reference wind turbine.

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.

Abstract. Numerical simulations of the Vestas multi-rotor demonstrator (4R-V29) are compared with field measurements of power performance and remote sensing measurements of the wake deficit from a short-range WindScanner lidar system. The simulations predict a gain of 0 %–2 % in power due to the rotor interaction at below rated wind speeds. The power curve measurements also show that the rotor interaction increases the power performance below the rated wind speed by 1.8 %, which can result in a 1.5 % increase in the annual energy production. The wake measurements and numerical simulations show four distinct wake deficits in the near wake, which merge into a single-wake structure further downstream. Numerical simulations also show that the wake recovery distance of a simplified 4R-V29 wind turbine is 1.03–1.44 Deq shorter than for an equivalent single-rotor wind turbine with a rotor diameter Deq. In addition, the numerical simulations show that the added wake turbulence of the simplified 4R-V29 wind turbine is lower in the far wake compared with the equivalent single-rotor wind turbine. The faster wake recovery and lower far-wake turbulence of such a multi-rotor wind turbine has the potential to reduce the wind turbine spacing within a wind farm while providing the same production output.

Abstract. This paper presents the integration of a near-wake model for trailing vorticity, which is based on a prescribed-wake lifting-line model proposed by Beddoes (1987), with a blade element momentum (BEM)-based far-wake model and a 2-D shed vorticity model. The resulting coupled aerodynamics model is validated against lifting-surface computations performed using a free-wake panel code. The focus of the description of the aerodynamics model is on the numerical stability, the computation speed and the accuracy of unsteady simulations. To stabilize the near-wake model, it has to be iterated to convergence, using a relaxation factor that has to be updated during the computation. Further, the effect of simplifying the exponential function approximation of the near-wake model to increase the computation speed is investigated in this work. A modification of the dynamic inflow weighting factors of the far-wake model is presented that ensures good induction modeling at slow timescales. Finally, the unsteady airfoil aerodynamics model is extended to provide the unsteady bound circulation for the near-wake model and to improve the modeling of the unsteady behavior of cambered airfoils. The model comparison with results from a free-wake panel code and a BEM model is centered around the NREL 5 MW reference turbine. The response to pitch steps at different pitching speeds is compared. By means of prescribed vibration cases, the effect of the aerodynamic model on the predictions of the aerodynamic work is investigated. The validation shows that a BEM model can be improved by adding near-wake trailed vorticity computation. For all prescribed vibration cases with high aerodynamic damping, results similar to those obtained by the free-wake model can be achieved in a small fraction of computation time with the proposed model. In the cases with low aerodynamic damping, the addition of trailed vorticity modeling shifts the results closer to those obtained by using the free-wake code, but differences remain.