# Computational Modelling of Rectangular Sub-Boundary Layer Vortex Generators
## 1 Introduction  
In order to achieve the aim of 100% renewable energy consumption, wind energy, as a leader toward the way of renewable energy, is developing rapidly all over the world. To decrease the levelized cost of energy (LCOE), the size of a single wind turbine has been increased to 10 MW nowadays, and it will increase further in the near future. Large wind turbines and their related wind farms have many challenges in aerodynamics, aero-elasticity and aero-acoustics. Therefore, the introduction of new designs and upgrading methods will be also needed to make this possible [1; 2]. According to [PERSON] et al. [3; 4] and [PERSON] et al. [5], either the use of passive controllers (vortex generators (VGs), microtabs, spoilers, etc.) or active controllers (trailing-edge flaps, synthetic jets and air jet vortex generators) can be introduced. One of the best options is the introduction of VGs on the blades to improve the aerodynamic performance needed. The use of this passive flow device helps to reduce the load distribution, and the blade has to undergo and obtain the optimal creation of energy. [PERSON] [6] compared the measured power curves with VGs and without on a 1-MW wind turbine. Although quite rough methods were used for the VG design optimization,the experiment showed that, for a [PERSON] wind turbine, power increased nearly 24% by using VGs through field tests. Furthermore, [PERSON] [7] conducted an experiment on a 2.5-MW wind turbine to test the effects of adding VGs on the power conversion performance. An increase of 11% in the annual energy production was found. In the work of [PERSON] et al. [8], Blade Element Momentum BEM-based computations were carried out on the National Renewable Energy Laboratory (NREL) 5-MW baseline wind turbine with and without flow control devices. The results obtained from the clean wind turbine without any device for flow controlling were compared with the ones obtained from the wind turbine equipped with vortex generators and Gurney flaps. A best configuration case is proposed, which has the largest increase of the average power output. In that case, increments on the average power output of 10.4% and 3.5% have been found at two different wind speed realizations  
VGs were first introduced by [PERSON] [9], and their principle of operation relies on the increased mixing between the external stream and the boundary layer due to longitudinal vortices produced by the VGs. Fluid particles with high momentum in the streamwise direction mix with the low-momentum viscous flow inside the boundary layer; therefore, the mean streamwise momentum of the fluid particles in the boundary layer is increased. The process provides a continuous source of momentum to counter the natural boundary layer momentum decrease and the growth of its thickness caused by viscous friction and adverse pressure gradients ([PERSON] et al. [10] and [PERSON] et al. [11]). Vortex generators can reduce or eliminate flow separation in moderate adverse pressure gradient environments ([PERSON] et al. [12; 13]). Even when separation does occur for cases of a large adverse pressure gradient, the mixing action of trailing vortices will restrict the reversed flow region in the shear layer and help maintain some pressure recovery along the separated flow. Thus, the effects of separation may be minimized or even removed. [PERSON] et al. [14] and [PERSON] et al. [15] studied the behavior of a rectangular VG on a flat plane and the streamwise vortices produced by them to investigate how the physics of the wake behind VGs in a negligible streamwise pressure gradient flow can be reproduced in Computational Fluid Dynamics CFD simulations and their accuracy in comparison with experimental observations. In the work carried out by [PERSON] et al. [16] and [PERSON] et al. [17] on a 30% thick DU97-W-300 airfoil (Delft University of Technology, Delft, The Nederlands), the maximum lift coefficient was substantially increased due to the implementation of passive VGs.