Development of nonlinear vortex lattice method for predicting wind turbine performance and wake structures

Abstract

Renewable energy has recently received considerable attention from both industry and academia. According to a study of the trends of renewable energy applications, the annual capacity of wind power production, including onshore and offshore systems, has been continuously growing in the past two decades. Wind turbines have become one of the most promising renewable energy technologies owing to their technical maturity and economic benefits. Hence, many researchers have tried to improve the energy conversion efficiency of wind turbine systems to achieve their more widespread use. A comprehensive simulation tool that can accurately and efficiently predict wind turbine performance is needed to develop more cost-effective and reliable wind turbine systems. Additionally, it is important that a numerical model can handle the various and complex geometries of modern wind turbine blades. Among the various existing numerical approaches, the vortex lattice method (VLM) is one of the most suitable models because the rotor blade mostly operates in the incompressible and subsonic flow regimes. Moreover, the VLM can represent various geometries of the rotor blade, including the camber, curvature, and sweep angle

however, it inherently cannot consider its nonlinear aerodynamic characteristics, which are mainly associated with stalled flow, yawed flow, and platform motions.

The present research is aimed at developing an aerodynamic model for wind turbine applications. In the current work, the nonlinear VLM (NVLM) is suggested to extend the existing VLM and handle the nonlinear aerodynamic behaviors that occur in the stall and post-stall regions. It is possible to apply the airfoil look-up table, correction models, and vortex strength correction to the VLM. The look-up table is an efficient and practical way to obtain the aerodynamic coefficients of airfoils for a wide range of angles of attack, and correction models help to investigate the stall-delay and dynamic stall phenomena. Additionally, the influence of nonlinear aerodynamic characteristics on the wake vortices can be considered through the iterative vortex strength correction. To obtain more accurate aerodynamic coefficients from airfoil tables, the location of the control point should be specified and the local flow conditions in terms of inflow velocity and effective angle of attack should be accurately evaluated. In this study, the location of the control point for NVLM is analytically determined by imposing the zero-normal boundary condition on the camber airfoil. Moreover, a time-accurate vortex particle method (VPM) is applied to represent the wake structures of wind turbines, and the wake-induced velocity is included for computing local flow conditions.

Numerical simulations of the MEXICO and NREL Phase VI wind turbine models are performed for the axial and yawed-flow conditions to validate the proposed method, and the predictions are compared against measured data. The comparison results show that the steady and unsteady aerodynamic loads acting on the rotor blades are well captured by the present method, even if the wind turbine is exposed to separated flow and highly yawed flow. The wake model is also demonstrated by comparing the tip vortex trajectories in terms of the radial and axial positions with respect to the wake age. The results show that wake structures consisting of Lagrangian-based vortex particles are well matched with the particle image velocimetry (PIV) measurements. Complex wake dynamics related with wake deflection, wake interaction, the tip vortex breakdown phenomenon, and transition into turbulent wake are clearly observed and discussed in detail. Additionally, the NVLM is adopted to perform the numerical simulation of an NREL 5MW reference wind turbine undergoing the prescribed platform motions, where both single and multiple degrees of freedom (DOF) movements are considered. The calculations show that the surge and pitch motions have a strong effect on the thrust force and power output of the wind turbine and the unsteady evolution of wake structures. The periodic deformation of the wake geometry causes a fast breakdown of the helical tip vortex structure and an asymmetric velocity deficit downstream. A wind turbine with a free-rotating rotor system is modeled using a simplified generator-torque controller, and its dynamic responses are evaluated at each time step by solving a single-DOF equation. The modeled controller is designed to maximize the power output by maintaining the optimal tip speed ratio. The rotor blade is free to rotate and its rotational velocity is determined based on the torque balance between the rotor and generator. The use of a free-rotating speed system has a positive effect in improving power generation and can potentially provide an attractive control strategy for wind turbines under unsteady inflow conditions. Moreover, the discussion in this work helps to improve our understanding of the fundamental control method for operating wind turbines and of the interaction between rotor aerodynamics and drivetrain dynamics.