Comparison of a coupled near- and far-wake model with a free-wake vortex code

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.