Implementation of the Blade Element Momentum Model on a Polar Grid and its Aeroelastic Load Impact

Abstract

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.

A simple improvement of a tip loss model for actuator disc simulations

“…The BEM model in HAWC2 has been compared with high‐fidelity codes many times. A comparison for the NREL 5MW in uniform inflow by Madsen et al showed very good agreement of the loading obtained by HAWC2 with results from CFD and vortex wake codes.…”

“…The BEM model implemented in the HAWC2 aeroelastic code is used as a basis for determining the constants of Shen's tip loss correction, Equation in this article. A tip loss correction by Wilson and Lissaman is implemented in the code.…”

Aero‐hydro‐servo‐elastic coupling of a multi‐body finite‐element solver and a multi‐fidelity vortex method

“…The basic BEM is modified to include wake expansion and swirl and extended with models to handle: dynamic inflow, skewed inflow, shear effect on induction, effect from large blade deflections, tip loss, and dynamic stall. The reader is referred to the recent publication of Madsen et al 44 for more details regarding the BEM implementation of HAWC2.…”

The effects of blade structural model fidelity on wind turbine load analysis and computation time

“…The turbine analyses for the presented work were performed with HAWC2 version 12.6, which is a strongly coupled aeroservo-elastic wind turbine simulation tool. The aerodynamic solver of HAWC2 (Madsen et al, 2019) uses the blade element momentum formulation (De Vries, 1979;Wilson and Lissaman, 1974) including effects of dynamic stall, dynamic inflow, wind shear on induction, tip loss, tower shadow and large blade deflections. A PID controller algorithm is used to determine the set point of the pitch bearing angle and generator torque.…”