# Study on Actuator Line Modeling of Two NREL 5-MW Wind Turbine Wakes
## 1 Introduction  
The flow passing through a wind turbine always makes the performance of its downstream wind turbine less efficient than that which was designed. This influence can decrease 10-20% of the production of the total wind farm [1] and increase 5-15% of the loading on the wind turbine blades [2, 3]. So it is significant to design the wind turbine by analyzing the wake-induced power and fatigue. Generally speaking, these wakes are very complicated and difficult to reproduce.  
There are usually two methods employed to calculate the performance and loading of the wind turbines. One is the Blade-Element/Momentum (BEM) theory [4, 5]. It is simple and computationally efficient, but needs to introduce some three-dimensional corrections, tip loss, dynamic stall, etc., to approximate the true situation. The other is the computational fluid dynamics (CFD) method. It can solve the physical problem accurately but always runs on a computer with consuming time. Despite this, many related researches on the simulation of the wind turbine have been documented by using Computational Fluid Dynamics (CFD) [6, 7, 8]. Besides, there also exist some other models that can always be used, including the actuator disc model [9], the actuator line model (ALM) [10], and the actuator surface model [11]. In these actuator models, the body forces are distributed in the flow field. Initially, the actuator disc model was used in the wind turbine far wake simulation. However, it could not reproduce the tip vortex system accurately [12]. Then, ALM was introduced by [PERSON] and [PERSON] [10] to overcome this difficulty, where the body forces were distributed radially along the blades and added to the three dimensional Navier-Stokes equations as the source item. Moreover, ALM is also an effective technique for predicting the loading on the blades with only simple structuredgrids, which has been proved by [PERSON] [12]. Recently, [PERSON] et al. [13] firstly proposed the concept of the elastic actuator line (EAL), which combines ALM and a finite difference structural model. In the EAL model, the elastic blades are incorporated into ALM and its simulation results are closer to the reality. Nevertheless, there still exists some limitations in EAL and this needs further study for the improvement of the theory of the actuator line.  
For quite a while, most models using ALM were realized by the in-house code, and there is very little commercial ALM software before 2013. Then, the National Renewable Energy Laboratory (NREL) in America developed a CFD tool called Simulator for Off/Onshore Wind Farm Applications (SOWFA) [14], which coupled the OpenFOAM [15] and FAST [16]. It contains the ALM and the atmospheric boundary layer (ABL) model. [PERSON] et al. [17,18] used it to simulate the wake of the two-turbine case and the result was accurate enough for a practical purpose. Recently, [PERSON] et al. [19] have developed a library named turbinesFoam, which uses ALM to simulate the hydrokinetics of wind and marine turbines in OpenFOAM. Its interpolation, Gaussian projection, and vector rotation functions are all adapted from NREL's SOWFA.  
In this paper, the contents of each section are organized as follows: Firstly, the concept of ALM is reviewed and the tip loss corrections [20] for the computations are given in brief. Then, an uncertainty analysis is carried out through a typical airfoil. After this, the single NREL 5-MW wind turbine case is used as the computational validation. Finally, the influence of the downstream wind turbine rotor speed and the separation distance between the two wind turbines on the whole system performance is examined. Moreover, the velocity fields in the wake flow are also analyzed. Considering the size of the domain, turbinesFoam is used to implement the computational task. The main reference data and the airfoil data can be found from the report of NREL [21].