Development of a Time-Accurate Viscous Lagrangian Vortex Wake Model for Wind Turbine Applications

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Gupta, Sandeep
Leishman, J. Gordon
A second-order accurate model has been developed and validated for modeling the unsteady aerodynamics of a wind turbine. The free-vortex wake method consists of the Lagrangian description of the rotor flow field and viscous effects were incorporated using a viscous splitting approach. The wake geometry solution was then integrated with the rotor aerodynamics model in a consistent manner. The analysis was then used to predict the performance and airloads on a wind turbine in the upwind configuration under unyawed and yawed flow conditions. The present work has demonstrated the versatility and robustness of the free-vortex wake method for wind turbine applications. The understanding of the accuracy and the stability of the numerical method is very important in developing robust wake methodology. The accuracy of the straight-line segmentation method has been examined for a vortex ring and helical vortex, and it has been shown to be second-order accurate. However, a minimum discretization of ten degrees is shown to be required to obtain second-order accuracy and also keep the maximum error in the induced velocity field less than 10%. Linear and nonlinear numerical stability of various time-marching schemes were also examined, and a two-step backward differencing scheme was chosen. The overall numerical solution was demonstrated to converge with a second-order accuracy. The nonlinear unsteady aerodynamics of the blade section was modeled using the Leishman--Beddoes dynamic stall model modified for wind turbine applications. The numerical simulations captured the dynamics of the unsteady flow over the airfoil surface for both attached and stalled flow conditions. Validation of the numerical predictions of the aerodynamic force coefficients against measurements obtained for the S809 airfoil showed overall good agreement. It has been shown that with a proper representation of the static stall characteristics, this model can be used to predict dynamic stall for airfoil sections typical of those used for wind turbine applications. The unsteady airfoil model coupled with the blade model also adequately represented the three-dimensionality of the unsteady flow field for a parked blade, under both steady and unsteady flow conditions. The wake geometry solution integrated with the blade model was then used to predict the performance and airloads for a wind turbine tested under controlled conditions. It has been shown that it is important to accurately predict the transient wake aerodynamics to obtain accurate estimates of the unsteady airloads and power output. The skewed wake geometry behind an upwind wind turbine was successfully predicted in yawed flow conditions over a range of yaw angles and tip speed ratios. Measurements from the Phase {VI} of the NREL/NASA Ames wind tunnel test were used for validating the predictions of performance and airloads. The variation of the turbine thrust and the aerodynamic power output with wind speed was adequately predicted. Spanwise distributions of the aerodynamic coefficients were represented well, and encouraging agreement was obtained against the measured coefficients. The azimuthal variation of loads showed that the unsteady aerodynamic behavior of the the wind turbine was adequately represented, with some exceptions.