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.

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Abstract. In the present work, a computationally efficient engineering model for the aerodynamic load calculation of non-planar wind turbine rotors is proposed. The method is based on the vortex cylinder model, and can be used in two ways: either as a correction to the currently widely used blade element momentum (BEM) method, or used as the main model, replacing the BEM method in the engineering modelling complex. The proposed method needs the same order of computational effort as the ordinary BEM method, which makes it ideal for time-domain aero-servo-elastic simulations. The results from the proposed method are compared with results from two higher-fidelity aerodynamic models: a lifting-line method and a Navier-Stokes solver. For planar rotors, the aerodynamic loads are identical to the current BEM model when the drag force is excluded during the calculation of the induced velocities. For non-planar rotors, the influence of the blade out-of-plane shape, measured by the difference of the load between the non-planar rotor and the planar rotor, is in very good agreement with higher-fidelity models. Meanwhile, the existing BEM methods, even with a correction of radial induction included, show relatively large deviations from the higher-fidelity method results.

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Abstract. We show that the up-scaling 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 disc (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 fatigue loads than the classical annular mean BEM approach. At high thrust coefficients 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.