# The Aerodynamic Analysis of a Rotating Wind Turbine by Viscous-Coupled 3D Panel Method
## 1 Introduction  
The Pacific island nation of Taiwan, having abundant wind energy resources, stable wind speed and direction, and shallow water depth, is listed by 4C Offshore Limited as one of the world's best offshore wind farm locations [1]. Taiwan has duly \"pledged to boost [its] offshore wind industry by investing NTS 88 billion (US$ 2.9 billion) by 2020 and NT$ 670 billion (US$ 21.7 billion) by 2030\" [2]. The island, however, being located in the northwestern Pacific tropical cyclone basin, is struck by an average of four typhoons per year, resulting in average annual total losses of NT$ 15 billion [3]. In August, 2015, Typhoon Soudelor alone destroyed eight wind turbines, causing \"an estimated NT$ 560 million (US$ 18.2 million) in damages\" [4]. The proposed wind farm units, in addition to the many typical failure mechanisms that afflict wind turbines in wind farms, such as exacerbated fatigue loading due to unsteady wind farm wake effects [5], will, therefore, also have to withstand typhoon-induced extreme loads. To better design for the wide range of loading conditions facing Taiwan's wind turbines, a fast, versatile CFD tool is desired, one which is able to handle the many challenges associated with theaerodynamic analysis of wind turbines, such as rotor rotation, rotor-tower interaction, wind shear, fluctuations in wind speed and direction, both ambient and self-generated (in-farm), aeroelasticity, and flow separation, which is unavoidable close to the blade root where:  
1. aerodynamic efficiency is sacrificed in favour of greater structural integrity; and
2. local tip speed ratios decrease with decreasing radial distance, resulting in higher angles of relative wind, and, typically, higher angles of attack. The CFD analysis of these detached flow problems is especially troublesome, necessitating a solution of the viscous boundary layer, which is achieved, in Reynolds-averaged Navier-Stokes (RANS) solvers, by very fine and therefore computationally expensive mesh resolutions near the wall, or, in potential flow solvers (panel methods), through empirical viscous corrections. RANS solvers, however, \"with their long computation times, which are typically in the order of hours [or even days for more complicated flow problems], are usually relegated to the post-design analysis of fluid dynamic problems, [while the] fast computation times of panel methods--in the order of seconds--make them an excellent CFD tool at the preliminary design stage\" [6]. A further advantage of panel methods over RANS solvers is that with the latter, a significant amount of time is typically required for preprocessing, such as mesh generation, watertightness testing, the clean-up process for which can involve considerable manual effort, and mesh independence testing. On the other hand, \"discretisation [in panel methods] is confined to the object's surface, allowing for fast, convenient modification of geometric parameters\" [6]. Finally, the speed and code-openness of panel methods allow for ease of coupling for such applications as aeroelastic problems, optimisation algorithms, and actuator line models, in which the reaction forces of the rotor on the fluid (equal and opposite to the calculated aerodynamic loads) are imposed on RANS [7; 8; 9; 10] or large eddy simulation (LES) [11; 12; 13; 14; 15; 16; 17] models of the entire computational domain of a wind farm. This actuator line approach allows researchers to investigate the unsteady flow field throughout a wind farm without the associated computational expense of resolving the Navier-Stokes equations around the individual wind turbine units. Such actuator line models usually rely on 2D airfoil characteristics at discrete blade elements for their input body forces, but [PERSON] et al. [18] observed \"larger deviations [from measured data] at high velocities where the flow field is detached\". The success of the current method in quickly and accurately modelling such detached flows makes it an ideal candidate for these actuator line models.