# Evaluation of Tip Loss Corrections to AD/NS Simulations of Wind Turbine Aerodynamic Performance
## 1 Introduction  
Wind energy is nowadays an important and increasing source of electric power. It has been the biggest contributor of renewable electricity except for hydropower, sharing about 5.5% of the global electricity production in 2018 [1]. As a primary subject of wind turbine technology, aerodynamics [2] largely determines the efficiency of wind energy extraction of an individual wind turbine or a wind farm. Along with the extensive development of high quality wind resources onshore, there are several trends in wind power industry: A large number of newly installed wind turbines have to be installed in areas with lower wind speeds and complex terrain; the layout optimization of wind turbine array becomes very important for wind farm design; offshore wind power development is accelerating, and the rotor size is continuously increasing. These trends need to be supported by more advanced and refined aerodynamic tools. More accurate aerodynamic load prediction is required for the design of a new generation of wind turbines with high efficiency and relatively low weight. Furthermore,a wind farm with dozens of wind turbines needs to be studied as a whole in order to take into account the complex interference between wind turbines. Blade Element Momentum Theory (BEMT) [3; 4] and Computational Fluid Dynamics (CFD) [5; 6] are two essential methods of wind turbine aerodynamic computation. BEMT is no doubt the key method for rotor design [7], while CFD gives the most refined data of aerodynamic loads and flow parameters. A full CFD simulation with resolved rotor geometry is usually employed for an individual wind turbine [8; 9]. However, full CFD is not suitable for a wind turbine array, due to the huge computational cost. The Actuator Disc/Navier-Stokes (AD/NS) method [10; 11; 12; 13] was developed for this situation, in which the rotor geometry is not resolved, and thus, the number of mesh cells is greatly reduced. AD/NS is based on a combination of the blade-element theory and CFD. The flow field is still solved by CFD, while the rotor entity is replaced by a virtual actuator disc on which an external body force is acted. If the blade entities are represented by virtual actuator lines, it is called the Actuator Lines/Navier-Stokes (AL/NS) method [14; 15; 16; 17]. As compared to AD/NS, the flow around the rotor solved by AL/NS is closer to the reality, since the rotor vortices are simulated. However, AL/NS requires more grid cells to describe the actuator lines, and thus, is seldom employed in wind farm simulations. The AD/NS method has played a significant role in wind farm simulations involving wake interaction [18; 19], complex terrain [20; 21], atmospheric boundary layer [22; 23], noise propagation [24; 25], etc. Nevertheless, the AD model assumes that the number of blades is infinite, and thus, no tip loss is simulated, causing an over-prediction of the blade tip loads and power output. In order to take tip loss into account, a reliable engineering model has to be embedded into the numerical solver, which is usually called tip loss correction. However, all tip loss corrections were originally proposed for BEMT, and there is no tip loss correction specially developed for AD/NS. Most of the literature about AD/NS simulations either did not mention tip loss or declared that the Glauert tip loss correction [26] was employed. It is worth mentioning that AD/NS and BEMT solve the momentum of the flow past the rotor by using two completely different approaches. The former employs CFD, while the latter applies the momentum theory, though they share the actuator disc assumption and the blade-element theory. That leads to different implementations of tip loss correction for the two methods. In the BEMT, tip loss correction is realized by applying a correction factor \(F\) into the induced velocity through the rotor. In the AD/NS, the velocity is naturally found by the NS solver, and factor \(F\) can only be used to modify the external body force.